I'm a very competitive person, but I don't mind losing. The fun is in taking part (otherwise, why bother?!).
The one thing I really hate is when you think that someone is letting you win. I hate that. It used to happen a lot as a kid. I knew what was going on and... well... if there's no real competition, there's no game. The whole thing is pointless.
I remember, when I was about five, my dad teaching me chess. Maybe it was because he'd just taken it up with his work colleagues and needed the practice, but he never let me win. He'd often warn me if a piece was about to be taken, but other than that, he played to win. And I LOVED it. I lost every time, but I really admired the respect he gave me in not patronising me. And then. One day I won. OMFG! One day out of hundreds, and I lost in every subsequent match, but it really meant something.
Another time (age 13?) I remember one of my parents' friends trying to bet with me that he could win a game of pool. I don't gamble (no problem with it, just not my thing -- it seems illogical), but he wouldn't take no for an answer. I reluctantly put up £1. It was a close game, but I lost. He then refused to take his winnings and gave them to me. I was furious (although I didn't show it). I couldn't understand why he'd pressurise me into gambling, and then not take the winnings. I felt like I was being made a fool of (although I could clearly see he thought of himself as the "kindly adult" playing nicely with the kids). We could have just had a fun game of pool, and he could have given me a quid, and I would have been delighted. Instead I felt like I'd been used as a tool for the bloke to demonstrate how fun and generous he was.