I'm generally pretty laid back, I think.
I'm only really ever competitive when it comes to video games, for one, and even in that I'm not always so competitive. I think that I become competitive when it's something that I feel I play well. I often don't like the idea of someone else playing better than I am in a game that I already feel accomplished in, and immediately feel challenged if they show more 'skill' in a sense of speaking. If I'm not so great, perhaps decent at best in a certain game, I'll often play casually. I don't feel challenged as I'm already aware that I'm not great in it. I subconsciously choose my battles, I guess. The better I am at something, the more competitive I become.
And finally, I'd hate to admit it but I become competitive (if only passively so) when it comes to my partner. I can be quite jealous, and I'd prefer to think that I'm always number one to him in every regard outside of his family. If someone does something that impresses him, and/or performs something better than I would, I would feel threatened. Call me self-conscious but it's sadly how I get. I want to be the one that impresses him the most, and I want to be the best in every way to him. The best that I can be, or better. So I often strive for greatness in this regard as I often crave his constant favor.
Other than these two scenarios however, I'm not very competitive in much else.