The list is almost endless but I will try to provide a summary of each so you can go and do your own research and come back and correct me! Where possible I'll add links to some of the better sites that I would trust.
The list is starting, explanations will come later:
Biconical
Birdcage
Bob-tail curtain aerial
Bruce Array
Cobweb
Dipole - fan
Dipole - folded
Dipole - half wave
Dipole - Inverted V
Dipole - vertical
G5RV
Halo
Helical
Inverted L
J-Pole
Log Periodic
Long-wire
Loop
Loop - magnetic
Marconi
Moxon
Quad - half wave
Quad - Levy
Quad - single element
Quarter wave grounded Marconi
Rhombic
Slim Jim
Slot
Vertical T
Verticals (sooo many types!)
W3DZZ
W3EDP
Windom
Windom
Wire
Yagi
ZL Special
And these are the tip of the iceberg!