My personal favorites:
Fallout: New Vegas
Terraria
Starbound
Kerbal Space Program (Don't have it yet, but I'm saving up for it)

Killertoad

the_pwnguinDay 1 Garry's Incident

Umm, for one, that game is horrible. Two, the devs are bad people, they were banning videos on YouTube, because youtubers were saying bad things about the game.

3. i was being sarcastic

Skyrim and Fallout 3 are both excellent games with an extremely large modding community with some fantastic mods. If you like RPGs, they'll give you hours if not years of game play without ever getting old.

Terraria is also really good and even better with friends. Some people might say it's the same as Minecraft, but those people haven't played it. It focuses much more heavily on exploration, dungeoneering, magic, and boss fights than Minecraft and includes a lot of really cool NPCs.

Paper Sorcerer is quite good as well. The price tag is really low and the game is great. This one can explain itself. It's just too good.
http://store.steampowered.com/app/263560/

I'm pretty sure you have this/have heard and thought of getting this, but I would recommend Skyrim. It is insanely good, and mods make it even better.

Other ones that are getting popular and have friends who said it is really good, is Rust, which is like Minecraft except more realistic-ish, and Papers, Please, which is a really interesting game where you work as a border patrol guy. Really deep.

Hope I helped

the_pwnguinDay 1 Garry's Incident

Umm, for one, that game is horrible. Two, the devs are bad people, they were banning videos on YouTube, because youtubers were saying bad things about the game.

Day 1 Garry's Incident

Castleminerz

X_pilot-snip-

Just wanted to say thanks, on behalf of many people, for making such a comprehensive list

You didn't specify what games you like personally, so I'm not going to recommend any, but I can give you some info on where to get cheaper games.

http://www.cheapshark.com/ http://isthereanydeal.com/
Both of these sites have a large list of games on sale from many different stores - with deal ratings and previous lowest prices. Very helpful to see if a game you want is cheaper anywhere else.
Everything I'm going to list here is a bundle site that all have some decent bundles and have new ones very commonly.
https://www.indiegala.com/
http://www.bundlestars.com/
https://www.humblebundle.com/
http://www.blinkbundle.com/
This is also a good site to keep up to date on any bundles in one list: http://www.indiegamebundles.com/

Trine is quiet goon its about 99 cents because its on sale

I love me some Gave Dev Tycoon.

Have you tried The Stanley Parable? Is a good game.

Any simulator.

Ive never played starbound but i here its basically terraria in space

I can name a few right off the bat.
-Terraria
-Don't Starve
-Blockland
-TF2
-Garry's Mod
-Spelunky
90% of these are paid, but they're normally on sale.
(Got all of em' for $15 on a sale. )

[deleted]

One game I'd seriously recommend to you is Just Cause 2 (if you don't have it already). There was an amazing multiplayer mod released for it a couple of months back on steam (you can download it just like a dlc, no hassle) and you could be in a game with literally hundreds of people. It is honestly mayhem.

However, if you're looking for a free to play game, I'd also suggest trying Loadout. It's a fun fast paced third person shooter with a cartoon-like art style, well worth a try. It's also not pay to win at all, as the only thing you can buy with real money is clothing for your character, no physical enhancements.

[deleted]

X_pilotMhhh...
-snip-

Thanks! I'll take a look at them.

Mhhh...
Ok. I know a few.
Star Conflict:
Space based strategy game where you must fly your ship in battle with a team. Going SOLO isn't an option.

Champions of Regnum:
Personally never played it, but it looks quite cool!

War Thunder:
Amazing WWII game where you fly as a pilot in different war situations. The game can be very arcady OR very very realistic. Massive battles are played with 60 people :O
I would 100 % recommend!!!

Dota 2:
Kind of like LoL...but different. (Not saying it's better!!!)

Serena:
Adventure game thingy...quite fun

The Mighty Quest for Epic Loot:
Just...wow...so amazing! 100% recommend!!!

Loadout:
3rd person shooter, however it is very brutal in a cartoony sense.

No more room in hell:
Zombies are rising and you defend yourself. Similar to L4D.

Haunted Memories:
I was so scared bro!!! I can't play it because I found a girl and I couldn't interact with her because I was ahead of where I was supposed to be. Great game though

March of War:
Strategy Based board game. Fun to play with friends

AirMech:
It's amazing...just try it.

Dwarfs F2P:
amusing for some time

Note: These are ALL F2P games that I have played and that are worth it. This is my style of game without the FPS...but yeah. I would have added FPS, but you specifically asked not to. I also thought I'd save you money!

If you want to spend money:
Rust
DayZ
Starbound
PAC-MAN MUSEUM

(: Thanks

Go google humble bundle and see if theres one going on. They usually have a lot of great games for cheap and the money goes to charity