Puddle of Mudd really isn't really my cup of tea, bit too much teenage angst for me, but to each his own as they say.
I can't say I've got a single favourite band and it would take ages to list all my favourites, but here are a few.
SchneiderTM
http://www.schneidertm.com/ - The future of pop music.
Lali Puna
http://www.lalipuna.de/ - Nico meets New Order in the 21st century
Solex
http://www.solex.net/ - quirky electronica from the Netherlands. Solex creates songs mainly from sampling the records she can't sell in her own record store. Her brilliant cover version of the Stooges 1969 can be downloaded from the site.
Adult.
http://www.ersatzaudio.com/ - The funnest, buzziest, punkiest, techno/electronica ever!
Chicks on Speed
http://www.chicksonspeed.com/index3.html - Does what it says on the tin, very fun :)
The Tycho Brahe
http://thetychobrahe.com/ One of my favourite Irish bands, capable of being intelligent without being pretentious.