In Muppet Family Christmas, Animal says of Cookie Monster- "That my kinda fella!" (After Cookie Monster demolishes and devours Janice's Christmas cookies). So yes, Cookie Monster and Animal seem to get along well.
Grover and Robin seemed to develop a friendship as well, seeing as Robin gave Grover a Christmas present with the Fraggle pebble (which is also a remote connection between Sesame Street and Fraggle Rock- though the Sesame Street gang have also interacted with the Fraggles some in The Muppets 30th. Anniversary special and Muppets Celebrate Jim Henson special.
Oscar seemed quite happy to let Rizzo room in his trash can, so that seems like a good pairing too.
Maybe Grundgetta could keep her own with Miss Piggy. (But to be fair to Piggy, it's not like she's mean and angry all the time.) She had some funny interactions with Big Bird when he guest starred on The Muppet Show. (And of course, there was the whole Gonzo and Big Bird thing...)
It'd be great to see a huge concert with the various Muppet Show and Sesame Street acts- Geri and The Atrics, the Gogolala Jubilee Jugband, Lubbock Lou and his Jughugger Band, and The Electric Mayhem playing together with Little Jerry and The Monotones and Little Chrissy and the Alphabeats and How Now Brown and the Moo Wave and of course, The Beetles.