Incredibly ugly but good games

Fallout :D

alien/zombie shooter series
deus ex 1
half life 1

The Witcher 2, because of how low I had to make the visuals to run it.

Cataclysm Dark Days Ahead
Minecraft :P

Betrayal at Krondor

*Note: I linked to the GOG version rather than the Steam one due to the fact that GOG currently has it on sale.

Ugly or old?

Alpha Centauri

Nidhogg

Dominions 4

definitely Minecraft

Defender's Quest before the recent graphics update.
Party Hard
Papers Please
Princess Remedy
Moirai (does this count? It's only 10-15 minutes long)

FF7 because graphics were an inconsistent mess. I really enjoyed the game despite the bizarre blocky character models that were used in game play & sometimes in videos. Other times like in battle, you had nice looking character sprites & in some of the movies too - guess they must have burned through budget or artists or maybe both really fast.

Tales of Maj'Eyal

(Even the name is ugly)

Deus Ex: Game of the Year is one of the best games ever made (imo), and there's already a fan mod called Deus Ex Revision, which to some extent improves the graphics by a full revamp of the game, and is freely available to all owners of the game on steam, if the bad graphics bother you.

Playing Deadbolt lately, and despite it being pretty ugly, it's challenging and fun.

• Original Deus Ex looked and sounded only average when it came out, and hasn't aged well in that regard. In terms of actual game, it's still rock-solid.
• Depending on your taste in graphical style, everything Vlambeer would count - their take on pixel-art is a love-it/hate-it thing.
• Dwarf Fortress (with default tileset)

Avadon and Avernum series. They are just incredible if just people could go over the graphics
One of my friends told me when Avernum 2 got bundled in the monthly "you spent 50 hours on that game, you're the only person I've seen spending time on that game. Why?" lol

NEO Scavenger

Ground Control 1.

Hotline Miami

hmm.. well i wouldn't call it ugly, but in the "incredibly minimal" games category i always recommend "Thomas was Alone"

way more fun then i ever thought it would be.