I guess I'm story-driven first-and-foremost. I just like playing through the games, defeating all the trainers and raising a team of Pokemon that I like.
Then I might start raising teams to be slightly more competitive... but nothing serious. Mostly just battles with friends and some random wi-fi battles. Also, a bit of shiny hunting. I guess I kind of do a little bit of everything to make my team more impressive without really going so far with any of it as to really be serious about it. :P
And then, sometimes, I'll go dex-filler, if I've decided I want to do that with a particular game. And when I do, I go all-out on it -- in fact, I've already successfully reached 100% Pokedex completion in Pokemon X (minus Volcanion, but that hasn't been officially released yet so I'm not counting it -- besides, as soon as it is officially released, I'll just get the event for it and then I'll definitely have 100% completion) and, more recently, in the 3DS eShop version of Pokemon Blue. And those were two... very different experiences. XD But both challenging in their own ways. o.o And definitely rewarding! Oh, and although I could have used glitches to get just about any Pokemon that I wanted in that game, I didn't -- I restrained myself from cheating (despite how easy it would've been, given my knowledge of Gen I glitches) and caught all of them FAIR AND SQUARE except for Mew, because it's literally impossible to catch without using a glitch...
SPEAKING OF WHICH: the last Pokemon that was added to my dex on Blue was Hitmonchan -- which I was stuck on for quite a while, by the way o_o -- and, upon reaching that point, the game thought I had already caught 'em all despite Hitmonchan still missing. o_o Though I wasn't too surprised by this, seeing as how I had already caught Mew by this point, and Mew was a last-minute addition to the game (hence why it's only catchable by glitch -- they didn't have time to program in any legit way of encountering it), soooo this means that there were originally only supposed to be 150 Pokemon, not 151, which means that the game counts having 150 Pokemon as a "full pokedex", even if there's still obviously a blank space anywhere between #'s 1 and 150. ...So uh. That's an interesting little tidbit of knowledge for you.
But I mean I still definitely went out and got a Hitmonchan because I mean saying I have a "completed" pokedex when I clearly don't is just a hollow victory -- no matter what the little certificate from the guy at Gamefreak says.
Edit: ALSO!! Professor Oak's reactions to you filling up your pokedex are hilarious. XD His pokedex ratings change as you catch more Pokemon -- specifically in increments of 10 -- and... yeah, it starts off with words of encouragement or hints or whatever, but, as you approach about 120 or 130 or so, his ratings start to take on a certain tone of... disbelief? XD It's like he didn't expect you to actually do it! (Which is probably an accurate level of expectation for the average player...) So... yeah. I for one found it incredibly entertaining to see him become progressively more shocked at how well I was doing as I inched closer and closer to 150. XD