I can't be the only one who tries to remember scientific names of ants by associating them with a descriptor. This is what I know so far, share how you remember them!
Linepithema humile - #$@% Argentine ants. The bane of my house every summer.
Pogonomyrmex - Harvester ants. Ant farm ants, probably the second ant I recognized as a kid.
Dorymyrmex insanus - Insane ants, called that for a reason.
Camponotus - Carpenter ants, fat queen, spidery looking workers.
Crematogaster - Heart butts.
Acromyrmex versicolor - Leaf cutting fungus farmers (though I've never seen in the wild).
Myrmecocystus - Honeypot ants you see on Nova, I've also yet to encounter.
Solenopsis - Teeny fire ants.
Veromessor - Black Pogonomyrmex I always see up around Bishop, CA.
Pheidole - Big heads. Yet to see in the wild.