Accelerometer to walk, tapping the screen to aim and fire. Obviously. :P

The only issue is that Quake just isn't Quake without frantic jumping and stylish manoeuvres, and you just can't replicate this properly on a touchscreen (neither on a gamepad). There are some interesting free games that run on the Q3 engine though (no extra data files required):

http://tremulous.net/
http://www.urbanterror.net/news.php