Let me take a different route with this answer. As already stated we have modern armor that is pretty effective against some bullets, called bullet proof vests. I want to instead discuss in more detail the plausibility of the future armor examples you described, and what future armor would look like:
TL:DR advanced armor's using modern techniques can be plausible, but many of the ones used in tv and literature is not practice.
Any armor provides some level of protection. A midevil suit of arms would give you more survivability from a modern day assault rifle blast then nothing. Quilted armor, even an extra layer of heavy clothing, can increase your odds of survival against a bullet blast...to an extent. The real question has never been can armor increase your survival if struck, but rather the armor's increased protection justified it. There are other costs to consider for armor such as:
movement: We limit our armor use now primarily because the old heavy armors of the past restricted movement. The protection of traditional armor, while nice if you got shot, was not worth the slowed movement which made it far more likely that you would get shot before you managed to shoot the other side. With the increased lethality of modern weapons when struck the focus is on getting out of the way, or killing your enemy before he can shoot you, rather then on absorbing a blow. Anything that slows your ability to draw and aim your weapon, or makes it difficult to move to a safer position, is most likely going to be detrimental unless it drastically increases your survivability when struck
Endurance: Old armor was heavy, and HOT. Someone could not wear armor all day. Heat strokes were actually a non-trivial threats to knights in long fights during the summer due to the heat of their own armor. The armor would exhaust them rapidly leaving them unable to fight, and leave them with bruises and sores from the way they wore it potentially. This is not an issue for swat or folks that throw on armor just long enough to, say, invade a drug cartel's warehouse and subdue those inside. However, if your looking for armor that is part of your military's standard uniform, as in worn in any remotely dangerous area even if immediate fights aren't expected, you need to make sure that you don't encumber them to much. Not only would it slow them down and make them less productive; you would risk them taking it off because it was too uncomfortable and then being attacked unarmored. It's a known issue that soldiers would not wear their helmets even on battle fields when they should, despite the protection it could offer, simply because they figured they weren't being shot at now and that helmets uncomfortable.
Expense: Like it or not, militaries are still ruled by money, as is everything. As far as a military is concerned you CAN put a cost on a life. In a real battle, where your desperate just to win, you are constantly making decisions not on how to save everyone, but how to get the most effective use of the lives you do lose, and if you calculate that for the expense of saving a few dozen lives with expensive new armor for all your troops your deploying you could instead put a down payment on a bomber that can blow up many dozens of enemies...well it is more effective to buy the bomber. Sounds cruel, but that's how you need to prioritize things to win a desperate war. Expense is going to be a major limiting factor with modern armor. Look at Iraq, where body armor, or lack of it, was a constant complaint. We had armors that could save lives, but it didn't get to the infantry because it cost too much (partially, see below). If armor is too expensive it will not be standard, but some elite units may still get it...
Logistics: you need to get armor to those that need it, and repair it. The latter is the key one, most modern armor works by absorbing the blow in a way that will damage the armor. Armor may take a few blows, but it will eventually need repaired, or more likely replaced, after it gets shot. You could imagine a situation in the future where soldiers start out all armored, but over a long deployment more and more become unarmored as their armor suffers damage severe enough to make it more liability then asset and discarded; but where they lack opportunity to resupply.
Why is this all relevant to future armor? well, mostly as limitations to the theoretical future armor we have. First, while traditional metal armors do provide protection when shot, we don't use them because their restriction to moment and endurance is so great that they are a liability. We do, however, have possible advanced armors as others have pointed out. For now let's look at the bullet proof vest as an example, see other answers for other examples.
Your notice all of these future-armor's are designed with the intent of being a viable asset to the wearer, and thus are designed with issue 1 & 2 in mind. They tend to be (relatively) light weight, and only armor the main body. That's because anything on the arms is likely to restrict your ability to draw and use your own weapon to a degree that they are more likely to be a liability then asset (similar issues with legs). Of course the other reason that arms and legs aren't covered is because it would require tailoring the armor to specific size of user causing logistics issues (see 4) and adding to expense of armor that isn't justified for the minor increase of survivability, since most lethal shots are to the body (see 3).
While helmets are standard issue for anyone in danger, limit effort is put into these. To be frank if you suffer a direct blow to the head your dead. It doesn't matter if the helmet prevents the bullet from piercing, the impact of absorbing that much force at one time is going to whip your head back so fast that your brain bludgeons itself against your skull. Modern helmets are not really intended to protect against direct point blank blasts, but against ricochet or shrapnel; which they do quite well. Helmet armoring techniques will no doubt improve, but it's unlikely that we will see standard physical helmets ever designed to save someone from point blank shots. Your notice helmets also never cover the face, any decrease to field of vision does FAR more harm to your odds of survival.
Finally, what most of the answers on this page don't address is cost. Modern body armor is expensive, expensive enough that it's limited. Countless police officers and military have gone into danger without armor because their precincts or platoons couldn't afford the armor. The fact is the biggest restriction to modern body armor is that it costs so much that many aren't willing to buy much of it. What you do have is often old, doesn't fit quite right (it's not sized for you!) and may very well still have damage from the last bullet it deflected; not to mention that it may very well have had blood one one side or the other of it from a past fire fight it was worn in. It's a large enough investment that you don't toss out armor until it's completely shot.
So what does this mean for out future military?
Well, it's likely that we will make these armors lighter (even modern body armor is pretty heavy, worth it for the protection but heavy enough that wearing it all day just-in-case would get tiring). We will likely also lower the cost of modern armor production. However, future guns will grow more lethal as well, so were have an armor to weapon arm's race.
Luckily I think we have more room to grow in armor production then we do in traditional gunpowder powered weapons. I think armor will grow cheaper while offering at least the same protection again body shots assuming were still using traditional gunpowder projectile weapons in the future.
However, even assuming traditional weapons the expense will still be non-trivial; and governments are still going to have to make cost-reward analysis. This means that future armor vs modern style guns will be limited by 3 & 4 considerations, and a little 2. Full body armor is unlikely, the restricted motion and general difficulty of convincing your solders to wear it even when not under fire is already an issue, but factor in the logistic difficulties and expense and it just won't be worth it unless we have a massive increase in our armor production abilities.
Body armor protecting the main body only may be plausible, but It seems unlikely that it would be worn all the time, if no other reason the soldiers complaining about wearing it while sitting in a desk in a guarded office. Instead Imagine it being worn only when you would wear a helmet now, when your in a situation where you believe battles could occur. That's if your lucky! Especially if set in near-future it is more plausible that body armor will only be provided to more elite units, your seals and swat or just your well trained elite platoons; but not your cannon fodder newbie infantry.
However, this assumes guns stay with traditional methods. Projectiles powered by other methods, such as electromagnetic powered rail guns may eventually become viable (they aren't now, but hey future, who knows). These weapons could have much higher muzzle velocities which could pierce armor better. However, how viable they even are, and how fast they will travel, is up in the air, as is how well are armor will develop. I would say that the only difference more advanced form of projectile weapons would have is that they would make armor less effective, but still viable. This would result in armor that is built to be less restrictive (less reason to trade off movement when you get less survivability from the trade) and generally seen as less cost efficient. Your more likely to have only elite units with armor in these cases.
Then there is the possibility of lasers or other 'future' weapon. In general... well I don't see it happening. However, I have no doubt we would develop armor designed to reflect the energy of such weapons, or even more active magnetic armors that repel the photons in some way, if such weapons existed. What they looked like or how viable they are is hard to say, as I said I don't consider lasers being viable so it's hard to anticipate how to protect against them since it depends on how one justifies their viability.
In any case remember that weapons will be designed with consideration of armor. If armor ever grew particularly effective we would start making weapons designed to pierce the armor. Were never have failproof armor (or if we did you would have to heavily reconsider the face of warfare).
So I've tossed you lots of future what ifs, since it's dependent on weapon technology and armor. How about a more general 'how to write armor in future fic' guide lines?
First, as I said full body armor is quite unlikely; especially anything that covers the eyes/face! If you have full body armor you will need to justify it by having armor be pretty cheap to make, cheap enough that your small scrappy good-guy team can afford some as well; otherwise it's doubtful everyone would have it. Though you could argue logistically the good guys can't get hold of armor that is otherwise cheap; restrictions set by government etc.
For full body armor if it is worn it MUST HELP!! It's soooo common to armor your bad guys, and then have them go splat to the first shot. If the armor is not saving lives there is no point in wearing it or paying for it. If you want armor of any type show it providing some protection. However, this does not necessarily mean that someone can brush off being shot. Anyone shot with a direct shot to body armor is probably down for the fight. They may have serious injuries that need treated, but at the very least the wind will be knocked out of them like the most vicious sucker punch, leaving them unable to continue fighting. It's okay to have your bad guys beaten by being shot while wearing armor, so long as you explain it as them surviving the blow to live to fight another day.
Of course a nicer version would be to have many shots being incapacitating, but also be possible to survive glancing blows with armor, and occasionally be shot and feel it, but keep fighting to some degree despite the pain because your armor protected you. The viability of armor depends on many variables, a blow may be lethal, incapacitating, or simply painful depending on exact angle, force of blow, and lots of other factors; so showing some variance in the effectiveness of the armor is more realistic and allows more room for interesting stories, the guy you thought was down manages to get up etc.
You are of course welcome to make even more viable armor, but if so show it getting damaged quickly as it blocks shots, and remember no armor is failproof. After all, a head shot is pretty lethal no matter what (but also very hard to hit, people will still mostly target the body unless your armor is unbelievably effective).
Remember armor takes damage and needs to be discarded as well. If you show armor as particularly effective at saving people then your have logistics of replacing them. This actually can be a useful thing to include in a story though. It adds some extra drama about resupply, if your lacking armor and feeling far more vulnerable. It allows you to show a team suffering from lack of supplies or just a vicious battle by demonstrating their lack of good armor or the damage their armor has sustained. You can also effect how dangerous foes are by controlling the availability of armor to foe or ally due to logistics or expense.
Showing more elite teams with better armor is more realistic no matter how the armor and weapons evolve. However, that's a good thing, it gives you a convenient way to visually identify the really dangerous foes by the amount of armor they wear.
Finally, There are lot of narrative advantages to giving your enemy masks, despite the fact that it's so restrictive. The best explanation would be to imply advanced helmets which provide an internal HUD, providing the same vision as no helmet but with tactical overlay. However, this costs money (as much with the cost of paying someone to develop the software to run the helmets and license it to you as with the hardware). The further in the future you go the more trivial the cost, but keep it in mind. It may not make sense for your average mook infantry to have expensive and complex headgear, particularly if they are going to lack other equipment that would be more useful (like...say basic grenades; which future soldiers on both sides rarely seem to have).
