Here are 20 ideas for games/toys I could prototype in UDK... possibly. (Disclaimer: this list includes almost every idea I've had up to now for senior thesis, so I reserve the right to pitch these again later on.)
Similar to ThatGameCompany's Flower, the idea is that you play as a little cloud, who drifts through the sky collecting water vapor and combining with other clouds to grow bigger. Different cloud types could have different behavior and/or abilities, and varying terrain or weather patterns could serve as obstacles.
2. Light-Sensitive Platforms
Platforms, walls or other constructs which are only visible/physically present when a certain color of light is shown on them; or, conversely, are not visible/physically present when a certain color of light is shown on them. This is similar to the ghost mansion levels in Super Mario Galaxy and probably a ton of other games that I can't think of right now.
3. Fairy Guide
You play a small fairy who must aid her human companion in his quest to save the world. Trouble is, your human companion is a ten-year-old kid with severe ADHD, so you need to keep him on track by helping him focus on enemies and pointing out and explaining important puzzle elements. Stay near enough to the baddies to keep your companion locked on, but don't get too close or you might get hit by some flailing limbs.
4. Lumber Jack
You are the notorious mountain man Lumber Jack! You wield a unique gun which uses entire tree trunks as ammunition. You can use these tree trunks to take out enemies in hilarious ways, or embed them into walls and use them as platforms to reach areas too high to jump. Chop down trees to keep your ammo stocked up.
5. Kite Warrior
You play a feudal Japanese samurai who glide on a large kite. Read the winds to control your movements and dive-bomb your enemies. Avoid obstacles that might cut the tether and leave you flying off to who-knows-where. I'm imagining these gliding controls working similarly to the cape in Super Mario World, or the wing cap in Super Mario 64.
6. That Ball-Tossing Game from TRON
There are a ton of different knock-off versions of the TRON motorcycle game, but to my knowledge no-one's ever made one of the Game of Catch to the Death that was shown earlier in the movie. Toss a ball back and forth and take out your opponent's platforms until he falls to his grisly demise.
7. Zen Runner
A simple platforming game with twist: You control a Zen monk and martial arts master, who is so in tune with nature that he can balance on the tiniest tree branch, a single flower petal, or a leaf floating on the surface of the water. Traverse breathtaking and serene environments as you master the art of balance and coordination.
8. Laser Whip
Okay, so you've got this super advanced futuristic laser whip. But, you can't just whip with it however, it will only extend to connect with these specially made nodes which are scattered throughout the environment. So to take out the bad guys, you've got to fire your whip, and then maneuver yourself to put your enemy between you and the node, so that they get fried in the beam. You can also use this whip to pull levers and swing over pitfalls.
9. Ground-Pound Hammer
You've got a giant hammer that's so heavy, when you smash the ground with it, it lowers the ground immediately under it by one unit, and raises all the within its area-of-effect by one unit. Manipulate the terrain to reach your goal and upgrade your hammer to produce wider areas of effect.
10. Wedding Crashers
This is an RTS-style game, where you control the family of the bride at a wedding of which they disapprove. Muster the forces at your disposal to sabotage the wedding without getting caught!
11. Demolition Man
You've got a limited quantity of explodey stuff with which to try and take down a building. Not the most original idea, but it's always fun to make things go boom.
12. Bumper Cars
One Wheel. Bouncy Cars. Crazy Tracks. Fun.
Fire-starters traditionally have little to no control over their abilities. You control a person cursed with pyrokinesis, trying to escape from the secret laboratory wherein you are being held. You've got a meter representing your fire powers, which you can activate for a limited time, but once you turn it on, who knows what could happen.
14. Marble Tracks
Everybody loves marble tracks.
You've got a gun that fires large, persistent balls of goo that stick to whatever they touch. Fire it at your enemies to stick them to the walls, floor or ceiling, or use it to repair bridges, weigh down a lever, or keep that little kid's balloon from flying away.
16. Clock Platformer
I really didn't realize how much I was pulling from Mario until I started writing this down. Okay, so you know that level in Mario 64 that's inside of a clock, and the platforms move faster or slower depending on what time is showing on the clock face when you go into the level. Same thing, except you've got the ability to speed up or slow down the clock parts at will, or even make them stop completely or go in reverse. Also make hourglass sand rise and fall to solve puzzles, or make a sundial jump forward to create shadows for stealth.
You start off as a sphere. You can roll. Once you reach a certain checkpoint, you grow a single leg. Now you can jump. Once you grow two legs, you can walk. With four, you can run. With eight, you can climb up walls. Finally, you grow wings and learn to fly.
18. Avalance - But in 3D!
Okay, so there's this flash game called Avalanche. You play this little marshmallow dude, and there are blocks that fall from the sky. There's also lava rising up from the ground, so you have to climb up the ever-growing tower of blocks in order to stay alive. So, that... but in 3D.
...This is pretty much straight up plagiarism and obviously I would never try to sell or otherwise present this idea as my own, but as part of a brainstorm and a potentially cool thing I could build in UDK, well, here it is.
19. Gradius/Galaga, but from the Other Side
You are the leader of a peaceful alien civilization being invaded by a self-centered hotshot in a shiny spaceship. Send waves of attacks at your opponent to defend your homeland. Earn bonus points elegant patterns of attacks.
20. First-Person Flower Picking
Walk around in meadows and woods, seek out rare and beautiful flowers and arrange them in a bouquet. Points awarded for pattern arrangement, color coordination, and rarity of the flowers.