Another 2D game I'd like to write (which might even be the same game as that one) is a bouncing ball game.
The player would be in control of a ball which could be accelerated by means of the direction keys. So holding down right would give a velocity increase in the positive x direction proportional to the length of time the key was held down (there have been a few games that work like this but in my experience in most non-simulation games the player only has one or two speeds and acceleration to/from these is instanteous). Wind resistance would be implemented to avoid the possibility of the ball reaching unlimited speeds.
Once the player has got used to these controls the next complication is maze traversal. While you could in principle just maneuvre around the maze slowly, it is much more fun to play at speeds close to the ball's terminal velocity. At these speeds, the ball's turning radius will be much larger than the scale of features in the maze, so the ball will hit the walls. When it does so, the obvious thing to happen is that it should bounce off (unless the wall is dangerous or special in some way).
Another possible complication is areas of the maze with gravity fields. The strength of the gravity could be smaller than the control acceleration (in which case it just changes the controls a bit) or could be greater (in which case entire directions become impossible to travel in). Gravity fields can be constant or central (or may have even more complicated configurations).
Then there could be places in the maze where the drag factor is proportional to some the velocity plus some constant field (i.e. windy places).
Some parts of the maze could be flooded with various different kinds of fluid, giving the opportunity to show off fun 2D fluid dynamics simulations.
Then of course there are the usual game elements - things to collect, power ups, space warps, spikes, enemies with various degrees of artificial intelligence and so on.