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

Cave story

Streets of Rage Remake
Warning Forever

Path of Exile (free on Steam)

The Spirit Engine II

http://www.thespiritengine.com/news.html

Tales of Maj'Eyal, one of the better roguelikes and unlike most of them has an ok UI and controls, a life system (optional), and most info need being clearly displayed. Can buy on steam, donate on site, or just download it free from the site. You only miss out on an extra class and cross character bank.

If do not mind using it there are also many good flash games, admitedly many of the best being TDs and JRPGs.

This site can be a good source. http://www.thefreebundle.com/

For card games there is Sol Forge, Hearthstone, Infinity Wars, and Elements to name a few.

For MMOs, well pick just about any that isn't WoW or Eve.

A few months ago SC2 went 100% F2P outside of campaign and some of it's ranked games. That means the large library of player made mods/maps are open to you now.

Well if you like flash games, Learn to Fly 2 ^^

Hearthstone

Mario on a emulator

Read that wrong... thought you asked for (non f2p) mmos.
Now I´m disappoint. :)

Nitronic Rush from freebundle.com

Super Mario Bros X - awesome game where you play Mario going throuh levels from few other SNES games. What is more - the game comes with real-time coop mode (yes, you are both playing at the same moment) which is really awesome imo. If you are into Mario games or were/are into old SNES/NES games, you should definitely try this game and you will most likely like it. The worst part is that they have closed down official website of the project so I guess it will be more difficult to get the game... Still possible I think, just look for other places maybe.

I will edit this post if I recalled any more but this is the only one I remember for now, sorry...

The Plan

Warzone 2100 If you need an open source strategy game (like C&C Generals but way better tech-tree and more fun).

TAGAP

I loved NAEV. You take you're bottom of the line space-ship and explore the galaxy doing missions, exploring storylines and crafting you're way into how ever you want to play the game. They copied it after EV Nova a classic in and of itself but 30 bucks is way to steep for that old of a game IMO. You can vote for NAEV here on Greenlight if you enjoy it. I await the day that blasted game gets on steam >.<

Heroine's Quest: The Herald of Ragnarok

Canabalt - Fun, simple game that's purchasable on mobile but free on PC

Little Fighter 2 - Brawler type game that I used to always play during middle school. There are also lots of great user-created mods for the game as well.

Super Crate Box - Haven't played it, but I found it just now and it seems interesting.

Red Rogue - Also haven't played/just found it, but it seems really intriguing and I think I'm gonna download it now myself. :D

Transformice

Umm... TF2 or Dota 2? No? Okay then... ( ik it's not indie )

You could look at Hearthstone.

Go to Desura.com, try out some of the free games there. I am pretty sure there are over 100 games there that are free. Some are crap but there are a few decent games there. Also http://www.thefreebundle.com/ has free bundles. At the top right of the page is a link to check out their old bundles and most of the links still work to get the older free bundle games.

Glum Buster - great pixel art and unique gameplay.
Hydorah - 16bit-style scrolling shooter, hard as hell and equally satisfying.
Battle for Wesnoth - probably the greatest freeware (and opensource) TBS, start with "Heir to The Throne" campaign to get the best impression.
5 Days a Stranger - don't mind the graphics, this point-n-click horror story has great characterization and clever puzzles.
White Chamber - another superb freeware point-n-click horror.
Iji - almost likeSystem Shock 2 in 2d, with Flashback-style graphics.
Notrium - survial on an alien planet.
DoomRL - easy-to-learn roguelike, now with graphics and mouse controls.
Also, early games by Nifflas (Knytt stories is probably the best), Spelunky (non-hd version is tons of fun).

Dwarf Fortress, Aurora Pentarch.

Dota 2

Open Hexagon