Hey, Acquiring the Taste! It's not the first album I'd recommend to someone new to Gentle Giant (rather Free Hand), but it's still quite interesting
For prog, Caravan's In the Land of Grey and Pink also came out in 71. Yes' Fragile too, but I actually prefer the album that came before (The Yes Album) and after (1972's perfect Close to the Edge).
Edit:
Wow, The Yes Album also came out in 71.. So 71/72 was definitely the time to be a Yes fan
Also Emerson, Lake & Palmer's Tarkus is a 1971 classic, though I think that will sound very dated to most younger people today.
Also, one could of course choose to avoid some of these well-trodden paths and strike out into less charted territories.