Something that can increase the cool factor of your game without really changing the game is a depth-perception-like feel when the user tilts the device. This can be seen in games such as Shadowmatic and Jump! Chump!, the checklist Wunderlist, or a lock screen background image with Perspective Zoom set to On. Although it's subtle, it can make your game feel a lot more polished and increase user engagement, as it's just one more thing they'll find cool or interesting about the game.
Tip
As a reminder, you cannot make use of device tilting/accelerometer in the simulator. It must be done on a physical device.
Here is Shadowmatic game's tilt effect seen on the menu. As you can see, it's a three-dimensional object, and the camera rotates around the object, as well as the shadows.
The first one is as follows:
The following is Jump! Chump! game's tilt effect seen in the game, where you can see the shadows of the main characters and enemies...