Genesis: Selling England... and Foxtrot
Yes: Relayer and CTTE (Relayer first! I have the feeling that, like I, you might not like CTTE)
ELP: Brain Salad Surgery, Trilogy
Random, more obscure but not totally obscure bands in assorted genres:
Van der Graaf Generator: H to He... (definately this one first; it's way more acessible than Pawn Hearts)
Frank Zappa: Hot Rats and The Grand Wazoo (Excellent introduction to Fusion. Nevermind that FZ is listed under Avant-Prog) Overnite Sensation for his more mainstream side
Jethro Tull: Thick As A Brick
Radiohead: Ok Computer, The Bends, Amnesiac
Tangerine Dream: Phaedra
King Crimson: ITCOTCK (everyone likes this, but I'm not sure why)