What games along the lines of Psychonauts, Beyond Good and Evil, Fahrenheit (Indigo Prophecy), Lego Star Wars, do you recommend?

Do you recommend Enslaved: Odyssey to the West?

My gamepad is a PSOne controller with a usb adapter.

My laptop:

Intel Core i3 1.7GHz
NVIDIA GeForce 820M 2GB Dedicated RAM
4GB RAM
Windows 8.1

ANYTHING LEGO.

Shovel Knight.

If your gamepad is good for fighting game combos, check out Guacamelee.

Elminage Gothic can also be played with a gamepad, but since that game is turn based and heavily menu based, it isn't nearly as important here.

Edit: You could also try the Ys games and Gurumin. Those games play nicely with gamepads.

Try the following games: Dust: An Elysian Tail, Ys Origin and Ys: The Oath in Felghana.

Is your controller a dual shock? If yes, I would recommend Darksiders 1+2 and Oddworld: Stranger's Wrath.

Enslaved works great using a gamepad.

I played Enslaved: Odyssey to the West with a PS controller and it was great, except for the aiming part, but that was mostly in the DLC from what I remember.

Dark Souls, baby.

Any console port ever released?

Besides the shitty quality of some of them.

Another one I just thought of: Geometry Wars (Steam link) is a very strong franchise of twin-stick shooters. It's about as pure as the genre gets, and it's tremendous fun no matter what your gaming background.

In general, yes. Enslaved is quite a good game, and is *much* better with a gamepad than with kb+m.

Risk of Rain.

Has Hammerwatch been mentioned? And did I spell that right? :P

A must to have a gamepad for and a lot of fun once you have that pad.

Tomb Raider series
Legacy of Kain series
Rayman series
Carmageddon series
Prince of Persia series

Agreed