Games that work by tilting your phone and require no buttons to be pressed are highly addictive, for example Resco Bubbles, a game that requires you to move your phone around to control a ball on the screen.
To play these type of games, your phone must have a G sensor built-in, listed below are some of the popular phones with Accelerometer:
HTC Touch HD
Samsung i900 Omnia
HTC Touch Diamond
HTC Touch Pro
HTC Touch Diamond 2
HTC Touch Pro 2
Samsung Omnia II (I8000)

Must have apps ;)
HTC Light Saber v1.0
http://www.freewarepocketpc.net/ppc-download-htc-light-saber-v1-0.html
Accelerometer Games for Samsung Omnia and HTC Touch:
Resco Bubbles http://www.resco.net/games/windows/bubbles.aspx
HTC Teeter http://forum.xda-developers.com/showthread.php?t=398494
http://www.noeman.org/gsm/pocket-pc-smartphones-games/78478-htc-teeter-game-samsung-omnia-accelerometer.html
G-Sensor / Accelerometer resources:
http://www.koushikdutta.com/search/label/Sensor%20API
http://sensorapi.codeplex.com/
http://www.c-sharpcorner.com/UploadFile/Vladimir84/G-sensor01062009002409AM/G-sensor.aspx