I'm sure this was done on here before, but here goes with mine....
Platys - Mr Orange, Mr Black, Mr Blue etc etc (from Reservoir Dogs)
4 (original) Tiger Barbs - Take That (NB Gary Barlow has since died)
Alpha male tiger barb - Five Bellies (due to sheer size of his stomach)
Can't think of any others in my main tank (although I'm sure they were given names when they were introduced) but my wife has the following in her coldwater tank -
Sid, Betty, George, Mildred & Freaky Frank
Slightly off topic, a mate once had a girlfriend who couldn't think of a name for it. It started off being called Little White Fluffy Cat.... it then grew up and became known as Big White Fluffy Cat... one day the cat went missing and much fun was had by the neighbours at the site of this grown man walking the streets, calling out "Big Fluffy White Cat.... Come here, Big Fluffy White Cat... come to Daddy"...