So far we have:
Oscars
Jack Dempseys
Angel fish
Compressiceps
Frontosa's
Butties
Blue Haps
Katoto
Tropheus Moori
Almost all American Cichlids (except Rams and dwarf species.)
Most African Cichlids (excepting shellies, rockdwellers and a few others)
Distichodus,
Piranha,
Red Hook,
Silver Dollars
Arowanas
Sharks (of any kind, Paroon, Irridescent, Silver, Columbian, Redtail, Rainbow, etc)
Clown Loach
Puffers (except Dwarves in species only)
Plecs/Panaques (Bristlenose and one or two others may go in a 20g)
Mystus Catfish
Redtailed Catfish
Tiger Shovelnose Catfish
Goldfish (not tropical but often mistaken for one)
Koi (same deal)
Stingrays
Knife fish of any kind
Bichirs
Bumblebee Goby (doesn't get big but are brackish, fragile and hard to keep)
CathyG is right. Too many to list not to go.