Beethoven's late quartets (especially opp. 131 and 132) are my favorites. Sublime. It's actually my favorite music of all time.
Shostakovich nos. 7, 8, 9, 13 and 15 are great, too.
And Barber.
And Haydn.
But Beethoven's quartets started my interest in string quartets... And made me write some.