Say there's some sort of apocalypse. A few hundred years from now, the ruins of our civilization will still be standing, but what about our technology? Obviously computers, robots and complex vehicles like planes and automobiles won't still be functioning after five hundred years without maintenance, but what about basic or crude firearms? Could the children of man one day unearth our lost and forgotten technology and discover the frightening power of the magic blasting wand of Remington? What about flashlights or cigarette lighters? Bombs and artillery like cannons or mortars?
I may reiterate some previous answers, but i'm also going to distinguish the reproducability of the technology.
Provided they are well-maintained, any firearm can be kept in working order for many hundreds (or thousands) of years. This is theoretically also true, provided they are stored in an air- and dust-sealed manner.
However, finer mechanics and technology will degrade faster, and will be harder to reporoduce. The more reliable and simple the parts are, the simpler they will be to exchange. In a post-spocalyptic world, you wouldn't go for the first, best, strongest laser rifle out there, but rather rely on a relatively simple AK-47.
There are much simpler weapons than this, like cannons used before the 1800s. They are basically just shaped cans of metal with a hole for the projectile to come out of, and a hole for the fuse. Even though such a cannon is not well maintained, it would still work for at least 500-1000 years.
Most aspects of, say, a modern assault rifle could still be reproduced (by reverse engineering) provided the finder(s) have the right eqipment for it, even in quite a degraded state.
Self-contained bullets and grenades (any type of modern ammo with included propellant) is unlikely to survive in working order for more than 100 years, as AndreiROM has mentioned.
The various chemicals used in gunpowder and more advanced alternatives break down over time, and may react in an undesired way, making the propellant not work, or very unstable.
Aditionally, modern ammunition is produced with precision in mind, you can't put just any ammo out there in a 9 mm gun without risking damage to the firearm (or the user).
On the other hand, an old Civil War era front loading musket with included ammo (lead or steel balls) can be perfectly stored away (again, in a sealed manner) and be usable hundreds or thousands of years later (provided the user knows how to make gunpowder)
You can have something like a combustion engine work for hundreds of years, but again, simpler things last longer.
A relatively simple engine from a moped or small motorcycle can survive for hundreds of years of storage (and even somewhat averagely-maintained use), another good example is an engine from a car like a Citroen 2CV, which were built to be easily repairable and basically unkillable...
On the other hand, a modern car engine (with arrays of sensors and other electronics) will not likely remain in proper calibration for long (maybe 5-10 years) and will likely fail completely shortly after that.
modern-ish Engines are relatively easy to reproduce, provided your people know how to make electricity (namely spark plugs)
Electrical utilities and tools
This again depends on the reliability of the parts used in the appliance. Any mechanical part will most likely degrade over time (unless protected against corrosion) and might need a bit of re-oiling. Simple electronics (especially resistive electronics, like toasters or boiler elements) can last for many hundreds of years, even in somewhat bad storage conditions.
The survivability of the different electrical components vary wildly, however, and the most susceptible parts are parts that rely on chemistry (batteries, electrolytic capacitors) and mechanics (servos and motors).
the reproducibility will vary based on the device. Most motors work on basic magnetics, while it'll be hard to reverse-engineer an SMD resistor.
Computers, smartphones etc.
Most modern (post-2005) computers could potentially work in a few hundred years (acceptable storage conditions provided), apart from mostly mechanical parts (fans, and HDDs usually get "sticky heads" after 5-10 years of storage). However, any solid-state component (basically everything on a modern PC component) will probably last indefinitely.
The reason why I mention PCs post-2005, is that the stable of using solid-state capacitors on compnents started around this time on enthusiast hardware.
Smartphones are basically ONLY solid-state components, so there's nothing preventing you from having someone find a smartphone in 400 years, rigging up a makeshift battery or 5v power supply and being able to use it.
Aaron comments: "However, I am highly skeptical of the claim that modern solid-state computer components could function after lying dormant for hundreds of years."
Again, this depends on how the computer is built, stored and maintained during its lifetime. And, yes, you do start to see 35-40 year old electronics out there that has failed or will fail soon. There are good candidates for long-lasting computers with easily reverse-engineered and very reliable parts, though; one of them being the classic C64. The 2 I have, are coming up on their 35th birthday soon and were both well-used machines when I got them, however, none of them have needed replacing parts as of yet. Not even capacitors. Should the capacitors have failed, it's still one of the electronic components that's the easiest to reproduce... albeit a bit hard to reproduce with exact values unless you have a multimeter or other ways to measure capacitance.
Yannicus comments: "I researched this a little (ie: lifehacker...) and SSD storage will degrade if it's not powered after a few decades. And that's only if it's in climate controlled storage...otherwise it'll corrupt much faster."
He is totally right. Electronic storage might be the biggest problem of longevity in all of computing. Now he doesn't say whether the storage medium gets permanently damaged or it's the data that gets corrupted. However, i've done some research as well, and the problem is with data retention as far as I can tell.
The data on the storage medium might not be able to hold the data, but other solutions are able to store the data for longer. For example, we have pressed optical media (LaserDiscs) already that has surpassed 40 years of age and still work, and even grammophone records that are coming up on 100 years of age.
And, yes, it's actually possible to press software or files onto grammophone records, by utilizing similar approaches as with cassette tape storage.
EDIT: Even though the thread is old, and I last edited my answer in 2017, coming back and reading the comments made me want to add a few points for future readers.
Firearms can last for generations - provided they are maintained, oiled, and stored properly.
A lot of companies these days ship their products in vacuum sealed bags, as opposed to slathered in cosmoline, or grease. Provided that the firearms were prepared for long-term storage, they could potentially survive for hundreds of years.
However, it's very unlikely for all those parameters to be met and maintained for 100 years.
This goes double for things like artillery pieces. They can last a long, long time, but that involves periodic maintenance and decent storage conditions. Most storage facilities are simply not meant to exist for 100 years without any sort of maintenance.
The problems with your scenario are many. For one, ammunition is very likely to decay in that 100 year span. Even if it was kept in optimal conditions, I certainly wouldn't want to be the one to fire it.
This is why the armed forces of the world routinely flood the market with surplus ammo while they renew their stockpiles. There's nothing wrong with surplus ammo except that it's 30 years or so old, and thus no longer considered absolutely reliable.
Ammunition is unlikely to survive in any decent quantity, and this holds true for artillery rounds as well.
You mention lighters and flashlights.
Flashlights run on batteries, and no battery will last 100 years. They're full of acid, and that doesn't recommend them for long term storage.
Lighters are not only prone to good ol' rust and decay, they also run on a fuel which evaporates quite easily. Could you find some preserved lighter, and a sealed can of fuel 100 years later? Let's entertain the possibility for a second: how would your character figure out how to refill and light the thing?
You seem to believe that "some sort of apocalypse" has a definite meaning. It doesn't. It's been suggested that the minimum size of the human population is about 50,000 individuals and that smaller populations are likely to go extinct. Its also been widely claimed that the death of 10% of the US population would lead to our country's economic collapse (deaths occurring at random, based on a DoD study of the 1950s or '60s). Without more specifics, your question is vacuous. Batteries (most currently sold today) won't last 500 years. Most plastics used today won't last 500 years (even in storage). So, without some sort of transitional society (using, maintaining, modifying, looting) to maintain a particular technology today, few of today's devices would (imho) function if brought out of cold, dry, storage in their original packaging, after 500 years. I'd expect a PC to work if plugged in. If a laptop wasn't stored with its battery, I'd expect it to work when plugged in also. Same with an LED (although if the plastic was cracked, it might not last very long). The central problem I have with your post is your assumption that all of the key technologies we have today will be lost. I'm certain that guns, internal combustion, and electricity would be almost certainly retained. I could list a dozen more almost as likely, but tell me: if you suddenly found yourself alone would you just abandon all technology? Of course not. Take a look at what the Cubans have done with US 1940's & 1950's automobiles. They weren't scrapped. They were used, reused, modified, fixed and upgraded. There's no reason a gun or cannon wouldn't survive if well protected from water and humidity. (Picture it submersed in oil). It is just false to say these things have to be maintained. Water exposure happens in several ways: most obvious by direct exposure to liquid water (rain, river floods, etc.) less obvious is by humid air and temperature variation leading to condensation (of course, some materials are directly sensitive to humidity). So, storage conditions are critical in this discussion. I know virtually nothing about the long term stability of the gun powders and primer compositions used today. It could be true that after 100 or more years the bullet wouldn't fire. I would invite anyone who believe 100 years would cause failure to stand in front of a gun loaded with such a bullet and allow someone to pull the trigger. There's two questions: corrosion and degradation. Without water, corrosion will be much reduced (I'm not willing to say eliminated, since the decomposition of either the primer compound or the propellant might lead to corrosive volatiles which could attack either the copper primer cap or the bullet casing) and the slow reaction of the ingredients in the primer or powder leading to either becoming inert. As I said, I'm not familiar with the chemistry: there's two possibilities:1) the decomposition products cause an increasing rate of degradation or 2) they don't. If they don't the rate of decomp will get slower and slower. Since I've used 10 year old rounds, I'm sure 1000 year old round will work under scenario 2. If scenario 1 is true, then I'm certain someone has studied it and the information might be public. The real problem I have is the assumption that the yokels in 2516 will lack the ability to make their own modern weapons. I think you need a "just so" story for that to have happened. Maslow's Hierarchy incorrectly (imho) put safety as less important than food, water, air and shelter. IMHO, its just as important, guns are a key technology and are almost certain never to be "lost".
It is highly variable. Not because we can't make technology that will last virtually forever, but rather because we don't as doing so doesn't make much sense to the people who make those decisions. The closer to present day, the more this is true, but further back before consumerism became as big as it is now, this wasn't the case.
If you can find an older cathode ray tube TV or monitor it'll work probably indefinitely. Cars, guns, etc will all work with a little cleaning. Batteries will work, but won't hold a charge that long.
The biggest thing that won't work is our electronics from the last 20 to 30 years. They will degrade from dirt, lack of power, and oxidation...plus most of it is designed to bio-degrade and break down as it is, but not all computers suffer from that problem, just most modern personal PCs, tablets, and the ones that most are familiar with. And this will probably happen within 100 or 200 years.
But it's no big deal really, because we do have repositories of most of the information on the web in physical format that is important and we have a read-only archive of the net that will last forever as far as I know that can be read with low tech stuff such as a light and magnifying glass. So really it would take a lot for a civ to fall beneath mid 1900s tech and even if they forgot how to do our modern day stuff, the archives could reteach them provided they knew the info was there and could read our language.
In an 'apocalypse', the greatest loss would be electric power. That is immediate, and all encompassing. I suggest you review the first episode of the James Burke series Connections - it begins with the potential fallout from a long term loss of electric power. A very interesting series to watch, if you can forgive the dated clothing styles.
However, with the knowledge base we have, it wouldn't take two thousand years to reinvent society. All it would take is some enterprising people who can figure out how to get electric power generated, so that all those useless devices can start working again.