Iter Vehemens Ad Necem, also known as IVAN. It's a roguelike, and the developers consider it a bug if you beat it.

I'll also second I Wanna Be The Guy.

Not necessarily indie but I recommend any older than 2000 games. GOG.com is a treasury of hard games :)

VVVVVV of course

and Hard Reset at maximum difficulty

Legend of Grimrock is pretty hard if you never played that type of game.

Super meat boy

And Yet It Moves, VVVVVV, BIT.TRIP Runner.

IWBTG
I Wanna Be The Guy

Oh, try to 100% The Legend of Zelda: Majora's Mask without a guide. I dare you.

Dwarf Fortress if you embark in the "right" locations =P

bit.trip runner, you shall ragequit alot!

Ikaruga - Dot eater the full game.

CoD

Super Meat Boy
Magicka - especially when you play alone
VVVVVV

Find yourself an emulator and try "Street Fighter 2010: The Final Fight." It was the source of my only broken controller while growing up.

Really Big Sky.

I wanna be the guy gaiden

old games like Barbarian, Gods, Ugh!, Prehistorik, Pandemonium and such are rather difficult :).

I CAN'T BELIEVE NOBODY HAS MENTIONED QWOP YET

if you want something silly hard then play with keyboard+mouse controls star wars the force unleashed until the star destroyer part :)

Hello hard game lovers! :)

LLC's hard games list:
Dwarf Fortress,
Super Meat Boy,
VVVVVV,
Red Orchestra: Ostfront 41-45,
Hack, Slash, Loot,
Killing Floor

Ultimate Doom on Nightmare.

Take any game, and play it on hardest settings.

So much more fun then playing on medium.

Super Meat Boy

Hard game :P