After reading that it's apparently much more convenient to play platformers with a gamepad, I tried to play La-Mulana and the Rogue Legacy demo with an Xbox controller, and it's a nightmare. Basically, I exchanged six fingers for an extra thumb, and that's a worse deal than the sale of Alaska.

So... what (DRM-free) games should I play to make some use of that pretty and useless thing?

Flatout?

pid for example, but be warned, it's pretty challenging.
http://www.gog.com/game/pid

Make sure you get the drivers for it.. ;)

They lied. The 360 d-pad is one of the worst I've come across on an official console gamepad and the d-pad is what you'd want for 2D platformers like those you list. The rest of the controller is decent, so I'm sure you'll find use for other kinds of game that are made to use the analogue sticks.

For 2D plaformers I use one of these: http://usb.brando.com/prod_img/zoom/UGAME001200_02_L.jpg
The d-pad isn't far off from the actual Nintendo ones (the SNES/N64 d-pad is hands down the best d-pad I've ever come across).

I haven't had any problems with the pad ever. I guess it's just a matter of getting used to the controller, if you've never held a pad in your hands before. The d-pad is useless, I give you that, but the analog stick makes up for it. As far as regular pads go, the 360 controller is one of the best in my opinion.

Just play more games with it and you'll eventually start to get the feel for it. I finished Rogue Legacy with it recently and I'm pretty sure I would've gotten tons more heirs killed with the keyboard.

If you can break away from DRM free and want a JRPG, try Last remnant. its infected with steam but comes on sale at gamersgate pretty often.

Wing commander, Freespace etc.?

So you like it?
I was wondering that I should install it after I played RAGE 10 minutes and saw that weird graphic system updating too slow.
But after a while it runs better and seems decent. So I might play it some more. =)

Infact I play it with xbox controller because it had some weird key settings. I couldn't put 'enter' to my use key and throwing boomerang thing with 'q' was like horrible. ^^

It's still thumbs-only, though, with movement keyed to the left thumb and actions to the right. I need at least one additional right thumb. Which games? In Rogue Legacy, I keep dying with ~200 coins to beginner monsters, not to mention a complete failure to do anything about a vaguely challenging environment.

I use a 360 controller and it works perfectly, I love it.

Maybe the game you are playing doesn't support the 360 controller, as I'm not familiar with the games I cant really comment, but it seems odd you would need many button combinations for a platformer.
There are gamepad programmes that you can use to customise your controller configuration, eg xpadder, maybe they would help, dunno if they work on a 360 gamepad though, I only used them on my old (Sidewinder?) gamepad..

But on saying that I have never come across a game (supported by the 360 controller) that the 360 controller was bad at.. Played TLR on the 360 a pretty awesome game, but a lot of people found it hard controlling their teams (nothing to do with the controller, just the mechanics).

Since recently getting an Xbox controller for my PC, I have so far enjoyed these games much more:

Rogue Legacy
Guacamelee
Retrovirus
Silverfall
A.I.M.

However, the last one points to an issue with older games - it does not honour the invert-Y-axis setting on the controller, even though it does on the mouse. This has made the game more difficult than it otherwise would be. So be warned that some titles that predate controller support may need additional stuff in place (like one of the controller wrapper programs) or may not support everything in the desired manner.

EDIT: Not sure why Rogue Legacy proved problematic for you, unless you don't care for the joystick-and-four-button combination of controls. The only thing I have trouble with in that game is the downward strike, but I was just as hopeless timing that on the keyboard.

Giana Sisters Twisted Dreams was also awesome with the Xbox 360 Controller.

Dungeon Siege 3 works also much better with a controller.