TTYD is my favorite. Its the first I played and the first RPG I played that had turn-based combat I actually enjoyed, because normally with turn-based combat it seems like the player has almost no control over the battle, and the bosses just feel like races to see who runs out of health first. There's still some of that feeling for me on the final bosses in the Paper Mario series, but the action commands make me feel like I can affect whats happening more than in other RPGs. Anyway, I just finished the original on my N64, and it's great and I loved defeating Bowser (I keep doing it over and over), but it just seems like everything was made better in the second game. For example, in the first they reuse the action command for Mario's hammer for like three of his partner's moves, and the same with the hold-down-the-A-button-until-the-red-circle-lights-up action command, but in TTYD every partner has their own "theme" for their action commands (Vivian's is pressing random buttons that appear as fast as possible, Koops's is hitting A with good timing, etc.). The addition of the stage and audience was a cool touch, and I like how parts of the stage will randomly fall down when someone uses a powerful attack. Also, I love the characters much more (Vivian's my fave), and I love all the places from the second game, and its got way more humor and Nintendo references and (IMO) better characters. But probably the best part to me is the story. I love the departure from the typical Bowser-kidnapped-Peach-oh-no-Mario-you-must-do-a-bunch-of-stuff-and-then-fight-through-his-castle-and-save-her scenario (don't get me wrong I freaking love it, and Bowser's Castle from PM64 is just plain epic, but I like that having a different main antagonist makes this game stand out). I think its great that Bowser was still a part of the story and you still fought him at one point, I think that was a very wise choice because Bowser is such a huge part of the Mario series and I love that they recognized that and didn't just cut him out in just to make the game good by making it "unique."
So that's why TTYD is my favorite Paper Mario game. If you're wondering why there's nothing about SPM, it's because I never played it. I heard that there was no turn-based action-command-enhanced combat, so I decided that my money was better spent elsewhere. Now that it's only twenty bucks I'll probably pick it up when I have the cash, but when it came out I just thought there were so many other games that I would rather buy.
I can't wait until Paper Mario 3DS (it's one of the main reasons I have a 3DS), but I've been watching the trailers, and I just don't know about the use of stickers to attack instead of the normal menus or about the lack of leveling-up by experience points. I'll just have to wait and see.