I'm a bit similar in respect to starting games and not finishing them.

It really depends on the games though. I'm a BIG RPG fan and have ALL the Final Fantasy games on the PS and PS2, as well as spin offs Kingdom Hearts and Dragonquest VIII.
I try my hardest to finish those games because I enjoy them so much. I didn't manage to complete FFVII or VIII but completed FFIX, FFX and FFX-2. Haven't got internet at home so can't get FFXI but definitely getting FFXII when it's FINALLY out, and Dirge of Cerberus etc...

I also enjoy my FIFA games. They're great because you can have a couple of matches every now and then and not have to COMPLETE it, like most games, because it just keeps going. Same goes for my Smackdown! games, you can play a few matches then go away.

So basically, I'm a keen player but I don't play as often as I used to. I usually play a brand new game for quite a while then leave it and sometimes go back to it later, but not always.