If a human is kidnapped by an alien vessel and taken to another planet - and, for the sake of argument, let's assume that the alien life-form lives in a completely different environment from Earth's.
Assuming, of course, that this alien race is far more technologically advanced than us, is it technically possible for the human to be "changed" in a way that he can breathe the planet's "air" (as opposed to Earth's) without dying?
To elaborate on bowlturner's answer, oxygen is uniquely suited for providing energy to large life-forms. It's one of the most effective oxidizers on the periodic table, (hence the term) and it can accept two bonds, unlike Fluorine and its friends. Digesting food is the process of burning it in a controlled manner to release the chemical energy, and you usually need some kind of oxidizer to do so. While there is more than one way to accomplish that oxidation, oxygen is so useful that an alien species is hugely likely to evolve the capability to process it, if it is at all present in their environment, even if they aren't carbon based lifeforms. And, too many of our chemical processes rely on it. You would have to artificially recreate a human from the atoms up to make them not use oxygen. Genetics alone can't overcome that hurdle in such a complex organism.
That said, as long as there is free oxygen present in the atmosphere, bolt-on adaptations to other toxins in the atmosphere are certainly within the realm of possibility. Alternatively, in a truly oxygen-free atmosphere, if the aliens didn't care too much about disfigurement or risk of explosion, you could have them grow an oxygen tank for your poor subject out of muscle and bone, with an umbilical cord of sorts fused to their nose.
To start with the human body is designed to run on Oxygen, and it would take a huge change, likely making us something else entirely if we needed to run on a different gas.
However, assuming you mean that the atmosphere is poisonous but still has Oxygen in it then it could be possible. Say the CO2 is extremely high, we could be redesigned to filter it out, or not absorb it through the lungs or maybe even have a converter to change the CO2 back to O2. Similar things might be done if other gases such as Chlorine were in the atmosphere at dangerous quantities, but special breathing apparatus could be used too, though not quite as useful since you still need to remove it to eat etc.
Actually, even a non-genetically modified human can already breathe quite a range of gases beyond a simple Oxygen/Nitrogen mix. There are numerous breathing gases that are in use, in a wide array of applications such as sea diving, mountain climbing, hyperbaric chambers, and spacecraft. The main requirements are: the correct amount of oxygen (within a certain range), and a lack of toxicity. Usually, breathing gases will contain oxygen, and some form of inert gas or gasses, such as Nitrogen, Hydrogen, Helium, Neon, or Argon. Even pure oxygen can be used. However, not all of these gases are useful for deep sea diving, because some (like pure oxygen, argon, or nitrogen) will become more toxic under higher pressures.
Oxygen is necessary, however, for practically every reaction that occurs in the human body, but especially by the brain. If there is not enough oxygen, the brain will suffer Hypoxia. Initially, this will cause a sense of euphoria, and an inability to perform complex tasks, shortly followed by passing out, permanent brain damage, and eventually death. Compared to the brain, the rest of the body is relatively tolerant of lower oxygen levels, at least for a little while. But it's still a critical factor for life.
On the other hand, if the body cannot eliminate enough CO2 (perhaps because the atmosphere already contains a high concentration of it, or is too dense to fully exhale), then the CO2 will form carbonic acid in the blood. This causes Acidosis, where the blood becomes too acidic, and can lead from headaches, to sleepiness, to causing cellular damage, to a coma, and probably death.
If you want your human to survive in a low-oxygen environment, there's not really an easy way around this, short of a breathing apparatus. Someone mentioned the possibility of a biological rebreather. I'm not sure if that could actually work, but it's one semi-plausible solution. Or instead, you might find a way to slow his entire body metabolism down, and put him in a state of hibernation or cryostasis, but he won't be conscious. You could perhaps replace his brain with a miniaturized computer, but then instead of oxygen, you need power. And if you can upload his mind into a computer, why keep the rest of the body?
Addendum: To show how forgiving the human respiratory system can be, as long as it gets enough O2 and gets rid of CO2, there have been some partially-successful experiments that demonstrate the possibility of breathing an oxygenated liquid. This mode of breathing has been postulated in science fiction for deep-sea divers, or astronauts in high-acceleration spacecraft.
Something else to keep in mind here: When you look at the possible chemical paths that support life things are quite limited. Looking at worlds with Earthlike temperatures there's only one viable pattern--carbon for the molecular backbone, oxygen as an oxidizer. Thus while the alien world might have toxins that need filtering out it's going to have the oxygen.
The standard sci-fi chlorine and fluorine based life simply doesn't work--both of these atoms are far less abundant than oxygen due to being less stable on a nuclear level and also created by far less common reaction sequences. Chlorine and fluorine both react with oxygen--for a world to have free chlorine or fluorine in atmosphere all the oxygen must have reacted with it and likewise it must have taken oxygen's place in the rocks. Most rocks are mostly silicon and oxygen. Thus you need an incredible amount of them and you're simply not going to find it. There's nothing else left to be an oxidizer, your aliens breathe oxygen.
Whilst your body is evolved to use oxygen its evolved to use it in quite a narrow concentration band. Too little and you pass out, suffer brain damage and die, too much and your nervous system is basically "oxidized" away and the resulting damage can be fatal. We need oxygen but we need the right amounts.
A person could normally have a space suit, we would make out of machery as an independent exoshell.
An advanced alien might make an adaptor out of living material and integrate it with our body, so it can transmit senses of touch etc and is self-maintaining and repairing taking material and energy from our blood. But it provides a rebreather to fit around the lung which still exchanges oxygen and carbon diodide, and provides a food processing system that transfers needed material to its own systems and produces compatible sludge to drop into the human intestine.
An analysis would notice a human body with a lung and stomoch removed and forign organs added and plumbed in; the skin removed and replaced with something that tolerates the outside environment; the eyes covered or replaced; the various openings sealed and plumbed into the support equipment instead.
Look at Fred Pohl's Man Plus for an example of adapting a human to live on Mars.
