One of the most challenging (and addicting) indie games you will ever try is Super Meat Boy. There you take the role of Meat Boy, the hero on a quest through hundreds of hazardous levels to save his girlfriend Bangage Girl from the mentally unstable Dr. Fetus. It's one of those platform games where perfect control and timing is crucial to win, it starts off easy but the difficulty scales up fast and soon enough you find yourself often dying (and if you're like me, cursing the world and smashing your keyboard) a million times before finally managing to get through some levels.
It's sort of reminiscent of I Wanna Be The Guy, albeit with the borderline-masochistic difficulty slightly tuned down. The game becomes specially hard if you're a completionist nut that just has to collect every single item, pass every single level with the A-grade time and unlock all the extra characters. But it's all in good fun.
I for one can't get enough of it, you probably won't be able to either.
The best indie game I've laid my hands on so far in 2013 has been undoubtedly Subset Games' Faster Than Light. FTL is a roguelike strategy game where you take on the task of managing a spaceship's systems as well as it's crew as it travels (and engages in glorious battle) across space.
The premise of the game is that your ship carries information that is vital to the space Federation and you must move across 8 sectors of space to deliver it, all the while trying to avoid the Rebel fleet that is hot on your tail. As you explore and gather supplies you can buy new equipment and make a variety of upgrades to your ship's systems.
Captain's log: We're all going to die.
The cool thing about this game is that if(when) the ship is destroyed, it's game over for you and that's that. This forces you to think carefully about everything you do, and ask God WHY when the tiniest mistake gets your loyal crew wiped out.