Maybe we shouldn't play Dawn of War?
But yeah, I can't say I've ever had this problem. Well, except in cases where I'm physically incapable of winning. I used to play Scrabble with my parents, but it was pointless because they knew more words than I did, so I always lost. Eventually I just said, "What's the point?" and we stopped. I wish I could take my Dad on now that I'm older. This was when I was like... 10.
That said, I generally don't care about losing. Probably because I do it a lot. Ask Sy. Every time we play Dawn of War he smashes me into the fucking ground with extreme prejudice. Every time we paint models, his look better. Every time we glue stuff down, he does 40 items in 10 seconds, and I end up gluing my hand to the table. So I think over the years I've just been conditioned to do the best I can. I'm not the best poet, not the best artist, not the best musician, not the best gamer... not the best anything. I just try to enjoy everything for what it is and enjoy the fact that I can participate. And then every now and again I manage to win, and that's always fun.
But yeah, I don't think there's a point in being overly competitive. All it'll do is make you angry. And the fact is, being less good at something doesn't make you less of a person. Most people are better than other people at *something*, even when that person beats them at the item in question. It's just the way of it.
I will, however, never play Super Smash Brothers Melee ever again. Ever. EVER. That was enough losing for a lifetime of loser-ness.