I won a fight and my crew dies away. There is no reason why! Nothing is damaged, no hull leak! Even if I send them to the medical station that doesn`t help! What a crappy game!!!

Oxygen might have powered down. Happens quite frequently when you are hit by Ion weapons or spend time in environments that limit your available power. Always keep an eye on your various systems!

On a related note, why are so many new users on these forums so quick to complain about a game or GOG as if the problem they are having are certainly a gamebreaking bug or GOG has sold them a faulty product?

I don`t complain about gog, I like gog very much. It`s not their fault that a game is so freaking hard! And, by the way, I didn`t say anything about a bug, I only wanted to know why my crew dies, although there seems to be no reason for that!
When nI said "crappy" I meant that a game shouldn`t be so.... programmed against having fun.

I'm pretty sure Sufyan is right, you ran out of oxygen, probably because the system hadn't got enough energy.

Ah, you've discovered the mysterious draining oxygen bug! Nah just kidding, there's no such bug. :)

Others have already said this, but most likely, your oxygen system is unpowered (can happen if system was damaged and you allocated the power to another system in the meantime).

Either that or you've opened all your interior doors and you have one or more Lanius crew members. Lanius drain oxygen from the room they're in, this includes the whole ship if all your interior doors are open.

Or you have a hull breach (you may have missed a small one perhaps?), which again should only affect the whole ship if you've got all your interior doors open.

Or you have all your interior doors open and one or more airlock doors. Opening your airlock doors tends to have the effect of venting the oxygen into space.

And please don't blame the game. The fact is, you have failed. If this were a real spaceship, and you somehow survived the suffocation of your entire crew, you would probably be court-martialled for negligence; if you died, you would win the Darwin Award (or be brought back as a Hologram some time in the future by the ship's senile AI).

If you don't have fun with this game, stop playing it, it's just not for you. Yes, the game is frustrating but it's what makes the fun, when you DO have success, it's much more rewarding than in very easy games. So yeah, you have to start over and over, it's the point of the game, you'll lose 95% of the time. And then you'll win. And then you'll win again because you'll know what to do. If you give up before that, it's fine too, the game just wasn't for you. But i can tell you this: it's not crappy. It's well made, the music is great and the gameplay mechanics work well...

TL;DR : try again. Dying is how you learn to play this game.

It`s not only the fact that I´m dying so often, it`s also the fact that the game gives you no manual. I`ve never seen a game without manual. I still love the time when games came with printed manuals, sometimes more than 100 pages and I loved the fact that you were able to put it on your lap and take a look into it whenever you needed some information during the game. But then came the time when companies didn´t want to print manuals anymore and put them as pdf files on disk. Nowadays it seems as if the programmers are even too lazy to make a manual.
And for the dying thing, you are not so wrong with this. I love to play Borderlands, where you die a lot times, too. But there is a difference between FTL and Borderlands. In Borderlands you have a chance in every battle, in FTL you can stumble across a very hard enemy very easy without any chance to win. That`s why I hated the early Fallout games,too. I always had random encounters with mobs that were too hard for my beginner party, after countles reloads I didn`t play them anymore.
To be honest, I think I´ll give FTL a try again, just because I want to kick the game in the ass!

It's not so hard after all. Just make the pause option your best friend, equip the right weapons to get through enemy shields and fire tactically for the biggest impact. Timing is crucial, so forget the auto-fire option.

As for the manual, there's an excellent Wiki for this game out there. Look-up some specific questions, but overall I'd advise to explore most of the game yourself. Learning how to survive is part of the design, e.g. like in Don't Starve. Extensive reading of solutions and walkthroughs spoils a lot. Also mind that this is an Indie game and it's probably better to spend the scarce resources on game development than on manuals, especially when a game is work in progress like FTL was for quite some time. You'll have a good time when you finally beat it, I promise ;-)

Just to check, was it:

1.) damaged?
2.) powered off (ion storms can and do drain power, which can power some systems off upon arrival, including oxygen)?
3.) being hit reliably by an ion weapon?
4.) hacked?

Based on what you have said, I'm honestly not sure what is going on, but the only thing that makes sense based on what you have said is #2; it's not enough that life support be functioning (which I can't is meant to refer to 'not damaged' or 'has an energy unit dedicated to it'), it also needs to be powered on. That and there *is* a tutorial; that should serve as a primer on the basic mechanics, and should provide a general idea on how to keep the crew from dying of oxygen deprivation.

It is not a bug, there are a few situations in the game that alters how much power you have available, the most obvious one being while fighting in certain nebulas that cuts down available power (the bars become blue and unavailable). You must pay attention to everything all the time. Pause the game at least once every minute to look at how your crew is doing, which doors are open, how your power is distributed, damaged systems and hull breaches. Every time you jump to a new place, read all texts carefully and make sure you understand what they are saying (for example, if a nebula is slashing your available power in half). Pause the game, assess the situation, adjust as necessary.

This game has a degree of randomness to it but if you feel you are at the mercy of it's whims then you are not giving it your best. You need to have an adaptable plan for how to deal with all the possible situations you may encounter. With experience you start to learn what kind of challanges you can typically expect from different kind of star systems and levels, and you have a loose plan for how to progress through the game, taking advantage of and changing the plan at a moments notice to make use of whatever the game gives you. It's a lot like playing a game of cards. The draw is random but you know which combinations are good to have so you try and leave a few good options open in case the right cards eventually get played on to the table. That's the best analogy I can think of actually, the abstract challange of FTL is a lot like building the best poker hand with what you have and using it to win.

If you think the game is throwing impossible encounters at you in FTL, it means you have not done all that you can to maximise your loot, scraps and load out. It means you progressed too far into the game without addressing a weakness in your ship design or crew selection. Same thing with Fallout, if you get killed in random encounters it could mean you have not geared up and developed your characters well enough to handle the area you are in, and perhaps you are handling the encounter all wrong. Yes, sometimes FTL and Fallout generate unproportionally difficult challanges, I'm not saying you can win every battle. I am saying that these are exceptional circumstances, they do not represent the true spirit of these games. If you know the dangers ahead (from experience), you should have a whole ABC of plans and a rough outline on how you intend to progress through the games.

In my current game I managed to get to the 4th sector. Luckily I didn`t encounter the "I lose oxygen without reason" event yet, but I fear this can only be a question of time. I hope that I will find an answer to this then. It`s strange that my crew doesn`t have space suits.
Since I played the game a few times now, I have developed a few tactics now, especially for Intruders! :-)

I was in the 5th sector, then a fire came, spreading from one fucking room to the other. When I fought it in one romm, it went to another. This is not fair, this game is really bullshit!!! And no, there where no sunburst and no enemies, just a nebula where the game said that it would disturb my sensors, not more! The developers are no humans, they must come from the deepest pits of hell!!
I won`t play this no more, this is not a game this is really a fraud!!

That's one way to do it. My best ship all time is named "The Fuckyouftl"... xD
Anything can happen, it's random so sometimes you'll get unlucky even if you played well you'll die. That's what makes the game fun, you never know if the next stop is going to kill you and you must be cautious.
Good luck !

As for your oxygen problem, were the doors open ? (silly, i know but you might have overlooked that parameter)
For the fires, use several guys to put them out faster. You can also open the outside doors which will remove the oxygen from the ship and thus put out the fire (you can do this with several doors to have only several rooms affected).
Rockmen are immune to fire, Engi repair at twice the speed...etc.

Just learn the game, you won't make those mistakes again.

Some weapons start fires on impact. If there are enough fires in a room, coupled with either using a mantis to put out the fire (or any other race if the fire has been burning for a while to the point it is almost about to spread) or low level/open doors, fire can spread quickly. My best guess is that you took a hit in a prior sector, which started the fire, and upon jumping into the nebula, you couldn't see the fire due to sensors being shut down.