Deeper and deeper - Mining game with some unique mechanic.

Leave something behind - Rougelite/Dungeon crawler where you can only hold a small number of items, so must leave some behind to pick others up.

Parasite - You play as a parasite that must latch on to other creatures and mind-control them to progress.

Shelter - You're a vampire that must carry a shelter wherever you go to protect yourself from the sun. - The zombie apocalypse has come, but your home is falling apart, you must keep repairing it to survive.

Expansion - Demolition game where you must make space for an expansion for your house. (ok, I might have got that idea from Teardown...) - Everything you touch starts slowly expanding/growing, and you must escape before you get trapped and squashed.

Hidden world - Platformer where you reveal hidden platforms with your mouse.

Delivery - Get X from A to B using some strange control mechanic.

You are the power source - Puzzle game where you power/activate certain things by standing next to them. - Shooter game with a weapon that draws it's power from the player's health.

Generations - Some evolution game? (really I can't think of anything for this one...)

One tool, many uses - You have some magic goo that can be shaped into anything you can think of, use it to overcome obstacles, as a key to a puzzle, or as a weapon.

Automation - You work in a automated factory, and need to program the robots to complete their tasks.

Lost signal - Your internet stopped working and you must find a way to fix it.

One time use - Shooter where every gun can only be used once before it falls apart.

Containment - Game where you herd animals/creatures into some particular area. - You must contain a corrosive liquid in a container by patching um the holes it creates.

Split in two - Puzzle game where you duplicate things by clicking them. - You control two identical characters at the same time, but in different places, you need to make sure both can get to the end without getting hurt.

Summoning - You play as a wizard and can summon monsters to fight for you. (yeah, not much creativity here...)