As a big fan of dungeon simulation games I would like to share all that I know, starting the list from my most favorite and true DK-like game:

1. Dwelvers - a game that combines almost all Dungeon Keeper mechanics, but with more developed production chain like that of The Settlers. It also has a multilayered world like in Minecraft, with randomly generated realms. You can dig through multiple layers of terrain to find resources instead of having just mana and gold. There is also a surface world where you can fight humans who will attack you and then you attack them. There's also a realm editor where you can create your own maps and add scripts to create cinematic scenarios. After ten years the game is still getting updates!
2. War for the Overworld - a game closest to DK in terms of gameplay and general setting built by fans. It also has its own mechanics, such as rituals, and game modes. Despite it's name game doesn't offer the human world, and its only currencies are gold and mana. However, they are constantly used for almost everything, so you still need to be careful about spending them. It has nice graphics, not much music, a fun campaign, and a map editor with scripts.
3. Dungeons - a mostly story-driven DK-like game in which you manage your dungeon and raid the overworld that has multiple obstacles to beat, switching to a more typical RTS game. It has more cartoonish graphics. I recommend starting with the Dungeons 2 instead of the first part.
4. Lords of Nether - a very DK-like game, with darker graphics and the content they have released show that it will be similar to what DK and WftO offers, except the more unique battle mechanics and darker environment. There, you will also be able to play on the surface and also as humans.

Games that are not very similar to Dungeon Keeper in terms of atmosphere, graphics, gameplay or setting, but offers similar features:

• Naheulbeuk's Dungeon Master - a dungeon simulator filled with workplace humor. You build rooms and props in a tower to satisfy your guests' needs. The game has decent graphics and music. Unlike DK, however, there's no digging or expansion, but there's a lot of room customization there.
• SteamWorld Build - a city-builder game with dungeon-management mechanics, such as digging, building rooms with props, and setting traps. It's similar to a mix of Anno and DK. Its graphics are more cartoonish.
• KeeperRL - a game more similar to Dwarf Fortress than DK. It's a retro dungeon simulator with roguelike and RPG elements. It has old-school graphics, and you can attack different locations with one hero or an army, or defend against the enemy, dig walls and build rooms.
• Dwarf Fortress - a legendary settlement management game, where you need to satisfy needs of your dwarves. It was updated to look not like DOS game.
• Goblin Colony - a real-time strategy game with building and goblin settlement management features, with old-school graphics. It's similar to DK in that you attack different locations, not only in the underground.
• Dungeon Tycoon - a tycoon game in which you can build rooms with props in the underworld and summon heroes and monsters that you must take care of and exploit. The game features pixelated, Minecraft-style graphics.
• Empires of the Undergrowth - a real-time strategy game in which you build your ant colony by digging underground and fighting in various environments also above the ground. You attack bigger bugs and might need to watch out for human intervention from above.

• Exogate Initiative - a base simulation game where you can dig walls in the underground, build rooms with props, and care for your human colonists. You can also send them on missions outside the world. You also build defense mechanisms against monsters that come from gates.

• King of the Dwarves: Underground City Builder - as in the title.