It's easier for me to indicate great string quartet composers than specific quartets, though with a gun to my head I'd either pick Beethoven's F-major "Razumovsky" quartet or Shostakovich's 3rd.

I have complete sets of quartets by the following:

Bartok
Beethoven
Brahms
Mozart
Schoenberg
Schubert
Shostakovich
Tchaikovsky

I also have Haydn's last three (eventually I need to hear more of them).

Debussy and Ravel also each have a great one (they're usually paired together on the same disc).