I came up with a bunch of random one-button games and control schemes I wanted to try before settling on one to run with. I'm sure other people did too. I'm never going to get around to making most of mine, so I figured I'd dump a few here. Feel free to grab something and run with it, or post your own ideas.
Some of this is might be obvious, but we've all been working in isolation (more or less), so I have no idea.
Grid-based selection systemI've been thinking about how an advance-wars style game would work with it. You'd basically have a 2x2 grid covering the screen, with one tap switching which quadrant is selected. Holding the button would bring up another 2x2 grid within the selected area of the larger grid. This smaller grid would be a 1:1 mapping to the on-screen tiles in that quadrant, tapping the button to switch between the four panes and a button hold to select a unit. Then the whole process would repeat to place the unit in a new location. For minimizing button presses, quadrants out of range of the unit would be grayed out and not selectable.
Puzzle cube gameHave a cube with a 3x3 (4x4? 5x5?) grid on each side. It rotates around the X-axis along a row of the grid. Button causes a colored marble to be put on the grid and for the cube to be rotated 90 degrees and move along the intersecting row on the grid. The colored marbles would be placed in sequence as shown in a "next piece" type thing on the side of the screen. The objective is to make matches of colors as large as possible. A match of three (four? five?) could be automatically removed from the grid and scored. Or a match could be scored when you drop another marble on top of an existing one.
If we really wanted to make things interesting, we could change the marbles to cubes and allow the player to stack them on top of each other.
If it's too hard to make matches of marbles, we could just have a dominant color per side of the cube and you'd get points for how many marbles of a color you got on a side. Maybe each side could have a "goal" color and the player has to get 20 marbles of that color per side.
Might need a max time limit before the marble would be automatically placed.
I guess the rotating cube idea is somewhat inspired by this:
http://store.steampowered.com/app/37800/I haven't played it. There's also a flash game where you're rotating a cube with stuff on it. I forget exactly what it was called or what the objective was.
Game: Spider SkydiverVertically scrolling game. There's a spider falling from the sky, leaving a trail of silk behind her. Pressing and holding the button causes the spider to stop letting out silk, causing her to swing back and forth. Releasing the button would cause the spider to use the momentum from the swing to move in the direction she was swinging. There would be a series of pegs placed randomly. If the silk touches a peg, it would stick to it. Some of the pegs would give points if you passed to the right or left of them. Miss enough of these pegs and you would get a game over.