Owlbear - a strange combo at first glance, but that strangeness helped define D&D as having its own sub-genre of fantasy.
Beholder - Another icon. Nothing says D&D like the beholder. A bit overdone in settings like the Forgotten Realms, but still capable of wowing newbs to the game.
Gelatinous Cube and Carrion Crawler - critters that either evolved to take advantage of dungeons, or were created magically. Either way, they are quintessentially D&D.
Rust Monster - Another highly specialized critter that seems to have evolved solely to vex adventurers. Again, pure D&D.
Delver - Oft-overlooked, the delver is a creature that helps rationalize all those caverns adventurers so love.
Bulette - a landshark, with dorsal fin and everything, that loves digging halflings from their holes. One of the first tough monsters my first PC fought against. Scary.
Displacer Beast and Blink Dog - the first monster rivalry that caught my imagination. Both had odd, and oddly similar, powers that made them natural rivals - in D&D logic, at least.