I try so hard to. But it's impossible to finish them all.
I never get bored of games. Hell, I love a lot of things. I just constantly switch gears. My favourite game this generation is Valkyria Chronicles and I haven't even beaten it because of all the damn games that distract me! Hahaha.
My parents set a rule on me when I was younger: you can't get a new game until you beat your current one. Well, Battletoads Double Dragon eventually came out, and that was a damn hard game. I eventually beat it, but I was like "enough of this crap."
Actually, I was pretty good about beating games after the N64 up to the Gamecube. When I branched out to Dreamcast I still beat games, and Xbox, and then PS2, and then a fuckload of games came out.
I guess my summary is, if you have all the platforms in a generation, you're never going to finish a lot of the games you buy.
I'm beyond repair now - too many RPGs to beat.

That, and over 150 gamecube games. I once sat down with my girlfriend and played every single gamecube game for 5 minutes - and it took two days to complete. However, I think I've finished a third.
Also, for the record, I was CRAZY about pokemon, but I never even bothered "catching them all." The only game I came close to 100% completion in was Chrono Trigger. I missed half the endings.