Anyone have any free (Non-MMO) games to recommend?

Super Crate Box. Already mentioned, but so awesome it deserves to be mentioned again. (Hey it's good enoug that I bothered writing up a review for it ;) )

Cry of Fear is a pretty scary mod.

(The updated version of the original-not the remake) Legend of Sword and Fairy/Chinese Paladin/Xianjian Qixia Zhuan Direct link to the download from the page

Legend of Cao Cao English patched

Can't believe I almost forgot Path of Exile.

Ib

Barkley, Shut Up and Jam: Gaiden

Exit Fate

Empires is a very unique free FPS-RTS hybrid on the free Source engine. Best vehicle combat on Source if you ask me.

"Hero Core" for true retro styled metroidvania-ish shootings.
"Gamma Brothers" just because of awesome arcade pixelcore shooterness.
"Deep Within A Forest" for oddly relaxing exploration-platforming.
"An untitled story" for surprisingly epic exploration-platforming (give it chance, it grows in scale).
"Treasure Adventure Story" for similar exploration-platforming, albeit not my favourite of the last three.
"Toribash" for freeform fighting with a steep initial learning curve.
"Dwarf Fortress" if you have patience, enjoy truer roguelikes (ASCII/tile form with complex mechanics and controls) and have a sadistic streak.
"IVAN" for the Dark Souls equivalent of roguelike games, plus crazy humour.
If you liked "Yume Nikki" and tried "Ib" as others have suggested, then perhaps look into "Mad Father" too. Not as good as Ib but still~
"Maldita Castilla" is another good classic-styled romp.

That's all I can think of at the moment.

Cry of Fear is awesome if no one has recommended it yet. I thought this game was a lot of fun since i like horror type games. I thought the graphics not being super amazing added to the suspense also