Many people new to Roleplaying find it hard to conceive of a game that does not involve any notion of winning and losing. The idea of winning and losing is so bound up with our concept of board or card games that anything else seems fantastic. Understanding the lack of a board and the use of strange dice is easy compared to the lack of winning.
Completing an Adventure as winning
Many newcomers, in fact, insist that there is winning, since the adventuring characters in the game go on quests, defeat bad guys, and 'win', or fail, die, and 'lose'. However this is not the case. In a roleplaying game the characters may indeed win, but the people playing those characters do not. They may share in the feeling of victory that their characters would have, but they have not 'defeated' the Games Master who set the challenges for them, rather they have worked with the GM to produce a good game, one which was a satisfying challenge to both players and GM.
Nor is it a case of 'beating the system', overcoming the world of the game. It is not the player who overcomes the 'system', it is the character, and the character and player, no matter how good the roleplayer, are not the same person. In any case there isn't even a system to beat. The GM is always free to bend the rules to make the game more fun. If a character's death would riun the game then the GM can ignore whatever killed him. To do otherwise is to put the mechanics, or the supposed world, before the enjoyment of the game and the gaming group, and that is surly to miss the point entirely.
Gaining levels as winning
Others acknowledge that there is adifference between character victory and player victory, but say that there is a deeper idea of winning, embodied in experienced point systems that 'reward' the players and allow their characters to reach higher 'levels' becoming more powerful in the process. This too is an understandable misconception. While it is true that there are some players who live to get more powerful characters (Power Gamers and Munchkins), this is, in the end, reductive. If all you want is a powerful character sheet to wave at people you could just go away and write it down at home. What people appreciate in a game is a good story, not the powers that they reach.
In fact, while most players enjoy seeing their characters increase in power it is usually because they feel afraid that something bad may happen to them if they cannot rise to meet new threats and adventures. All that new skills an abilities do is increase the challanges for the player and make the game more interesting.
Furthermore many players even hate to see their characters gain experience, because higher levels remove them from the mundane world and place them against more exadurated dangers. These players actually prefer low level characters and low level games. It is for this reason, I think, that many systems have now rejected the entire concept of levels, just because they are so uninterested in what might look like a form of 'winning'.
Telling a story as winning
The essence of an RPG is in fact a cooperative act of storytelling. Pretensious as it sounds it is true, you would be hard pressed to find a game where the players did not feel that they had a right to shape the plot, to inject details and suggest new ides to the GM, and if you did then like as not those players would not be enjoying that game very much.
Indeed in most games the GM will build half his plot as he goes along, extrapolating from the suggestions and guessings of the players. If a player, for instance, conjures up the threat of some monster or plot that the GM had not put in, then most GMs will put it in, just to prove the players right and to give them something to worry about.
The only way to lose an RPG, then, is to disrupt the shared-fantasy of the game in such a way that it falls apart (e.g. as is done by those bored players who resort to killing other Player Characters or who ignore the GM completely and waste all his preperation work). Otherwise, if you enjoy the game and the characters, then you have won.