These are the ones I pick and their nicknames (what we call them):
Hen of the woods (Sheephead)
Meadow mushrooms (Field mushrooms)
Morels
Oysters - these are very hard to find nowdays
Honey mushrooms (stumpies) - my least favorite
Aborted entoloma (undeveloped form - shrimp) (fully formed - grays)
Puffballs
Chicken mushrooms (sulfurs) - I don't really care for these. Some people love them though.
Picking most of these mushrooms were passed down from generation to generation. I haven't tried too many new ones.