I've never had "catch 'em all" in the broadest sense as a goal. I do catch lots of stuff in the games, just because I like to try everything out and I like to play the games working out of a pool of good pokemon, rather than just using a single team. But I don't go out of my way to catch post-game stuff (other than the stuff that interests me) or trade or any of that just to complete the dex.
I guess my overarching goal is to put together a pool of the best possible versions of whichever pokemon appeal to me most, then, out of that pool, to put together the best possible team for whatever I'm doing at that moment. I spend a lot of my time hunting for the right pokemon (Synchronize is a blessing - at least it's much easier to get the nature I want than it used to be), then sorting out good movesets for them, then assembling teams out of them, so I can make it through the next stage of the game easily (in spite of the fact that I'm pretty much always underleveled), and find and catch and train some more pokemon.
I don't really have a goal of beating the game, or even of beating the E4, really. I just make my way through the world and eventually end up there.