My favorite memory of Pokémon Colosseum was grinding for the non-storyline arenas. It took an assload of time to grind the six Pokémon that took me through the Elite 4 in Ruby to Lv100 for Tower Colosseum, and I didn't really know about IVs or EVs (or strategy) so you can imagine what kind of team it was. At the last match of the doubles tournament, up against a Kyogre and others, I had to face the reality that this team was just not going to win. So I got a Tyranitar and a Latios, EV trained for the first time, slapped a Soul Dew on the latter, and grinded them up to Lv100.
Finally got through that to the much awaited Orre Colosseum, and to Doubles. When I got through the matches to the last battle, a similar thing happened as before: I got my ass handed to me by an obviously better team. Burned through continues to the last one. Somehow I managed that battle to get down to my Tyranitar vs. his Latios + Slaking. Now, for some reason I had Protect on Tyranitar (Yes, Protect is valuable in doubles, but I sure as hell didn't know that when I put it on), and after a misclick on it, I put two and two together and realized that I could abuse Slaking's ability and focus on Latios. Somehow I just managed to beat Latios, and with almost no HP I whittled down Slaking too.
I think I wrote about it that day in a freaking diary. It is 100% of the reason that I learned to love double battles.
My favorite memory of Pokémon XD was the Battle CDs. That was exactly what Pokémon was about, strategy and logic. BW2 has sort of the same idea with moviemaking, but it still has a ways to go. They're on the right track, though.