Any damned part he wants!
The man is an actor and a very good one at that.
Shakespeare's plays are adaptable--that is part of why they are still being produced. And if Helen Mirren can play Prospero (a nan) in The Tempest, Mr Dinklage should have no casting issues.
Here are some of the parts I'd like to see him in:
Feste or Malvolio: Twelfth Night
Benedick: Much Ado About Nothing
Oberon, Robin Goodfellow, Nick Bottom: Midsummer's Night Dream
Hal the Prince: Henry IV
Hal the King: Henry V
Titus: Titus Andronicus

I would have loved to see him as Richard III

And just like the real Reagan, nobody is steering

John Green's repeated mentioning of "moist" reminded me of this little issue: http://www.youtube.com/watch?v=HgGcwbtQTss

Mixing male and female words can be hazardous!

I just know, somewhere in that race some one was shouting "Push The Button, Max!"

https://www.youtube.com/watch?v=R3Igz5SfBCE

Cowboy Bebop?

How about The Beatles' album Abbey Road(1969)?

Boy, you're gonna carry that weight
Carry that weight a long time
Boy, you're gonna carry that weight
Carry that weight a long time

LENNON / MCCARTNEY

I had a college History professor Dr. Dumin, who loved Hogan's Heroes. His parents fled the economic chaos of Weimar Germany moving to the US in the late 1920s. After losing almost everything in the Great Depression, they returned to Germany. Then the Nazis rose to power. My professor was 16 when World War II broke out. He spent the war dodging the draft and Nazi authorities. His older brother got drafted into the Wehrmacht and after the war, spent 15 years fighting to regain his US citizenship. Dr. Dumin was a great fan of the show. He was always quick to point out that Stalag 16 was run by the Luftwaffe NOT the Nazis.
In fact, the Nazis on the show were feared by Colonel Klink and his staff. He also loved to point out the uniforms were remarkably accurate for TV. Colonel Klink wore a Pour le Mérite (Blue Max), Iron Cross, Ground Assault Badge of the Luftwaffe, and the Parachutist Badge; and Sargent Schultz wore an Iron Cross, and were therefore not entirely inept cowards.

Documentary? On which planet?

No wonder they are so chewy . . .

Cool pictures.
But this wasn't the first time The Muppets visited Twin Peaks:
http://www.youtube.com/watch?v=Vftf8TTve4s

It is also distorted by a lack of knowing where the states are.

That is just plain WRONG!

I mean, where is the bacon wrapping??

Whats the matter with this guy? Couldn't he find a Ford Falcon?