Who has refused membership offers and when did it occur? The ones that i know of are
Ant-Man (Scott Lang)
Avengers 1999 he later joined
Peter Parker, the Spectacular Spider-Man #90
Avengers Vol. 1 #111
New Avengers #3
Avengers Vol. 1 #221
Avengers Vol. 1 #252
West Coast Avengers Vol.1 #1
Avengers Vol. 1 #216
Spider-Woman (Jessica Drew)
Avengers Vol. 1 #221 she later joined
Only other one that springs to mind is the Beyonder, he always seems to be missed off these lists. Cannot remember the exact issue but sure someone here will.
Then there are also those heroes who were rejected for membership, but thats a different kind of list.