So, here's some of them. Please don't rip me off. (Consider hiring me as an actual game designer though! I'll work much cheaper than that Shigeru Miyamoto guy! And I can actually program and make actual game art and music and so on! That's, like, a lot more than Miyamoto-san!)
Bruno the SlugosaurA sweet little girl (who happens to live in a huge automated mansion) has a pet, a giant slugosaur (a carnivorous brontosaurus-slug hybrid) named Bruno. One day, Bruno breaks out of his cage and starts to rampage around the mansion. Your task, as one of the mansion's hapless cleaning drones, is to clean up after Bruno while trying to herd him back into his cage.
The cleaning drone can only move by sliding along metal surfaces; most environments have parallel tracks for drones to follow along, but Bruno's rampage has caused a lot of them to break so you have to jump between different tracks to keep moving. And in the deepest darkest bowels of the mansion, there's no rails, just metal pipes to try to cling to, and so on...
Every now and then, the little girl (who is watching everything from her bedroom monitoring station) will send the drone electronic messages for advice, or will get on the PA to try to calm Bruno down.
I did a little bit of preliminary concept art for it, though it really didn't catch the graphical style. (Think brightly-colored flat-shaded late-80s computer animation, only using modern techniques like shadow maps and alpha blending and environment maps and so on.)
(unnamed game)I actually had this dream a long time (many months) ago but still think it'd work pretty well for a game.
Remember the classic 2D shoot-em-up games like Ikari Warriors or whatever? That's the basic play idea here, except that you control a small mecha as part of a large battle fleet (and can give commands to your fleet for which enemies to focus on). You yourself wouldn't have much firepower overall, but after each battle through some environment you have to unlock a stasis field which contains the next important thing for whatever this recovery mission is about.
The unlock sequence (at the end of each level) is, basically, Tic-Tac-Toss, where you have to (while fending off enemies and so on) lob "energy packets" at a grid in order to replicate a certain pattern.
Thaddaeus FrogleyRemember the bits in Super Mario 3 with the frog suit? Think of that basic gameplay, as a good old-fashioned underwater platformer, where you control Thaddeus Frogley who is on a quest to save his younger brothers and sisters (who are still tadpoles) from the evil bass fish. There'd be the usual platformer dangers, but you also have to watch out for water currents and so on. Also, by eating enough, you power up a "turbocharge" which lets you swim twice as fast (but only half as accurately) until it drains. Sort of a frog berzerker rage.
(Yes, he's named after Thaddaeus Frogley.)
Various puzzle gamesHow about a version of Columns except where the bottom of the game area deforms under weight, which you can use as another way to form combos?
Also, there's a puzzle game I started to code a long, long time ago but never got around to finishing which was along the lines of Columns, except rather than dropping 3-tuples of blocks into the field, you push them in from the left. The prototype was fun to play; a pity it was done in Turbo Pascal (which dates it at 1997 at the latest, since that's when I finally switched to C under UNIX) and I have no way of compiling it anymore. Well, I do still have TP around somewhere, but it also made use of the crt library, which is notorious for having a (totally pointless) timing loop in its init code which causes a division by zero error on anything faster than a K6/233.
Also, I'm sure there's a way to combine two of my favoritest puzzle games of all time, Puzzle Bobble and Mr. Driller, into something mindlessly addictive.