I'll get on board this one too. For me, there are two consoles that really would have suffered without some takey-turny Mario action: the GBA and the Gamecube.
Mario & Luigi: Superstar Saga was the first Mario RPG I ever played. It was hilarious. Fawful was a great character, and the supporting cast poked fun at the bros. in a way Nintendo had never really done before. ("Did you see that?" "Yes. Moustache.") Moreover, the battle scheme was different to anything I'd tried, and it worked wonderfully well.
The later M&L games have still never really recaptured the magic of those Bros. Moves for me. In fact, they never captured the magic again at all, relying on much the same things that had to be new to be appreciated for how great they were. But when they were new, they were wonderful. While I would have enjoyed the GBA without M&L:SS, it was one of my favourite games on the console, and I still look back fondly on it.
The Gamecube is my favourite console ever. Including LoZTP, it has more in-my-opinion-10/10 games than any other console: the others were SSBM,
Metroid Prime, and
Paper Mario: the Thousand-Year Door. And the last one may just be the best of the bunch. I played it through twice, once with my sister, so that we could both appreciate the beautiful world unfolding (ha!) before us; and no game has made me love the GC more, or seems more representative on a console of great yet unsung games (apart from on here, natch).
I missed the original
Paper Mario, too young to appreciate the "boring" RPG genre when it came out and too set in my ways to try games of genres I "knew" I didn't like; so again, TTYD was a new experience for me. The "stylish" system added a wonderful new dimension to battles, Mario's papery transformations worked so very well, the partners were brilliant and lovable sidekicks, the story as a whole had an epic scale and oft-entertaining dialogue that charmed me almost without stopping, and the locations and set-pieces! The Excess Express! The Glitz Pit! Doopliss and the letter "P"! And yes, Rogueport was a brilliant hub-town. Still one of my favourite games ever, although I find it very difficult to reconcile the fact that a character my young brain found "sexy" was anatomically male in the Japanese version.
The others didn't have the same effects. I missed both
Legend of the Seven Stars and
Paper Mario the first times around, and neither had a great impact when I did play them, outshone by their ancestors as I felt they were. In the later games, the Paper Mario series went too far away from its apex, and the Mario & Luigi games stayed too close to it, as well as adding misguided 2D sections into the mix. Neither has found their heights since, and none of them would have really taken away from their consoles in their absence.
In fact, perhaps the other Mario RPGs would have had a bigger impact on their consoles if they
hadn't been released. The Wii would have paled in comparison to the 'Cube without a Paper Mario, the DS would have seemed emptier without a Mario & Luigi, and I'd never have known that the games that weren't would have been so disappointing in comparison if they were.
Best supporting character (as I recall) in PM was Watt. Best in TTYD is tougher - probably Vivian once she learns Fiery Jinx, Bobbery before that.