I got Sakura Samurai, Ketzel's Corridors, and Dillion's Rolling Western all free through Club Nintendo (remember Club Nintendo? Pepperidge Farms remembers). That was a while ago so I don't remember them particularly well.
Sakura Samurai: If I remember this game correctly, the controls were making swipes on the touch screen to swing the sword in various angles, aiming to use the correct ones to hit enemies. It's a pretty simplistic game with little variety, it was okay as a freebie but I don't think I'd spend any money on it. I recall the last boss being pretty ridiculous in a bad way.
Ketzel's Corridors is a concept I believe I've seen before with at least one other game, but can't recall the title. It's basically moving around a 3D Tetris-like piece so that it can fit through a set of walls which are heading towards the camera. The latter stages move at crazy speeds, I don't think I could clear every level. It's a decent action-puzzler, but again I don't think I'd have paid for it, meself.
Dillon's Rolling Western is a game / series I wish I could like, but it has some major problems holding it back. It's a fairly unique concept to mix tower defence with action, and there's a little bit of exploration and discovery in searching for resources on the maps. The two main issues are that the combat is extremely repetitive, and that you barely get any money the first time you play a stage, allowing for building hardly any towers and have to fight everything yourself. Breakable equipment was definitely a mistake for this game as well. This is yet another good example of a game which would benefit from being shorter and having much less padding. Still, due to its uniqueness and being a new (at the time) IP from Nintendo, I'd still recommend checking it out. Maybe people would like it more than I did.
I played the Wii version of Art of Balance, which is a fun little physics-based puzzle game. I believe the 3DS version has the same puzzles at the Wii one, plus maybe some new ones added too but I forget. It's worth a try on any system, though on Wii it used the pointer which I liked. Touch screen would probably be okay though.
I tried only the demo of Mutant Mudds. Retro-inspired games are not for me, and this was no exception.
Always been the most mildest of curious about Dillon's Rolling Western. That game got physical releases in Australasia/Europe/Japan, but never in the Americas. Just seems odd for a Western themed project.
You're confusing this with the most-recent, third game in the series. The first game - which is in this poll - and the second game, are exclusive to the eShop in all regions.