Its late and I'm about to go to sleep so pardon the crude nature of this post I hope it is still helpful. I'm basically going to spew ever computer game related thing I do for fun.
A note almost none of these have the world manipulation combined with MMO style game play like Haven and Hearth does but if your just looking for games I think these are fun.
Specific Games (majority single player unless you have a group):
Terraria: I consider worth the ten bucks.
Minecraft: Oddly hasn't been said.
Project Zomboid: Its in way early beta, give it a shot and just check on it weekly til they get a save function and a couple other basic features and it should become a rather fun game.
Dwarf Fortress: Suggested above, like Haven and Hearth there is no built in tutorial but unlike Haven and Hearth its not intuitive like other games.
NetHack: Endless fun. I've never made it to the end of the game but I still have fun trying. Like Dwarf Fortress it somewhat un-intuitive but once you understand all the commands and what symbols are what (or learn to have the wiki open) you should be fine.
The one multiplayer game I've really kept up with and still fully enjoy when I have time is: Kingdom of Loathing. The game may be showing its age now but then again it was never intended to last this long and it started out more as a joke. The biggest plus I have with this game is that the developers do a regular podcast on game development twice a week where you get to hear (among other banter) a large amount of the internal dialogue that happens.
You can also always start doing competitive gaming. And I'm not talking about Starcraft or any top-end MMO stuff I'm talking about setting up a metric to measure the quality of a play through of a single player game and then competing. The perfect example of this is speedrunning where you base it solely upon time from start to time of finish. I never got to far into actually doing runs but the planning alone can get insanely intricate especially when you start talking about risk to reward where you want to prevent burn out so you show multiple scenarios. I'll point you to
http://speeddemosarchive.com/ as a good place for this. Warning though they break several games and much like we many people in this community relish the cries of people who get randomly killed and rage about it they will relish you complaining about how not playing within the guide path is not "fun".
Oh and competitive Pokemon is always an option:
http://www.smogon.com/ Its at least an interesting idea.
I don't believe any of these cost more than 20 dollars and the majority are free. Hopefully you enjoy at least one of them.
A.K.A. Suddo