I know there have been roguelike threads before, but I recently went to play ADOM and discovered tilesets had been implemented within the last year. I was surprised, couldn't find a thread here about it. So I'm sharing. Lately I've been playing (all with tiles):

Ancient Domains of Mystery
Dungeon-crawling, much randomly-generated. Was ASCII forever. Almost 20 years old!
http://www.adom.de/

Unreal World
Great sandbox-wilderness-survival set in iron-age Finland. Older than 20 years! As of now, 3.17 is the latest stable release, and you can slightly improve the tileset with a custom pack in the forums. My favorite. Good tutorial.
http://www.unrealworld.fi/

DoomRL
Now with tileset!, and awesome DOOM soundtrack remix and sound effects. Dungeon-crawler with guns, rocket-launcher and a chainsaw, pinkies, etc.
http://doom.chaosforge.org/

Cataclysm: Dark Days Ahead
Zombie apocalypse, sandbox, crafting, vehicles, guns, spears, bionics, mutations, portals and creatures from the nether. Highly configurable. There are a number of tilesets available in addition to those included in the base package. Increasingly left4dead-style special zombies, but you can also set it to just classic Romero zombies.
http://en.cataclysmdda.com/
edit: wanted to add that the STALKER OSTs make a nice background for this game.

More games with tilesets, like Tales of Maj-Eyal, Dungeon Crawl Stone Soup, and Nethack, of course.

Thank you for this awesome thread. I've recently started playing Tales Of Maj'Eyal. Another awesome roguelike people should check out. In this game, you could be slaying rats and snakes for 5 minutes then all of a sudden an undead skeleton warrior mage comes out of nowhere and you are like "OH SHIT!". And then this undead skeleton warrior casts 10 spells on your character instantly so your character can't move and is weak, then eviscerates your character, forcing you to restart with a new character or rage quit.
http://te4.org/

PS
The game is free so you have nothing to lose.

All are free!!!

It wasn't when I last played.

However, there is a chatroom built into it, so you can talk to others who are playing the game. You can also link special enemies and items you encounter to chat, so others can easily view attributes, etc. So it's a single-player game, but you needn't feel you're playing all alone, if that makes sense. These features are optional, I expect.

edit:
I'm surprised to see ADOM with a tileset!

Damn, Adom looks sweet. I used to play it for hours back when it originally came out. Gotta give it new spin.

And even better, they've even added music on Adom. Hot damn.

No love for rogues?