When playing video games, I rarely care about actually beating the game, or winning versus other players. This weekend I played a bunch of Civilization 5 and is a great example of what I wrote above. I don't worry about the score of the game, or even the victory conditions. For me, Civilization is all about the journey. The same goes for most strategy games I play.
Speaking of Civilization, there is not much better than starting a new game. So much is unknown about the world around you. Which resources are nearby? How close are the other empires? What is the geography like? Getting those questions answered is part of what makes Civilization a great game.
There are exceptions to my not caring about winning, of course. League of Legends is one game where I want to win. I even find it hard to play Normal games because I know I could be spending my time in ranked matches instead. To spend 45 minutes in a match just to lose it ends up being pretty demoralizing. But a win is oh so sweet.
In scenario based PvP ( WAR, SWTOR et), I really don't mind losing. There is still character progression (forward, not backwards like LoL), and as long as the match was fun I am happy.