Note from author: I wrote this back in 2012. I don’t know if it works anymore. Be sure to check out the other more recent answers.
Amir’s answer got me close, but you need the ACQUIRE_CAUSES_WAKEUP
flag at least (Building against Android 2.3.3).
WakeLock screenLock = ((PowerManager)getSystemService(POWER_SERVICE)).newWakeLock(
PowerManager.SCREEN_BRIGHT_WAKE_LOCK | PowerManager.ACQUIRE_CAUSES_WAKEUP, "TAG");
screenLock.acquire();
//later
screenLock.release();