I had a friend who made a Dunmer character and joined the Stormcloaks. He says it was really fun "breaking the mold".
These are my characters and their alliances. I try to fill out my characters with nearly completely different skill sets, perspectives, and gameplay styles. It helps me touch all the corners of the world.

Hyva Skull-Splitter - Nord - Battleaxe - Stormcloaks
Vierna Teken'duis - Dunmer - Dagger & Destruction - Neither
Garakh Shadborgob - Orc - Mace & Shield - Empire