Formal:
* Exile
* Exiled person
* Exileé (for a woman)
* Emigré (used specifically for political exile)
Informal:
* Outcast
* Banished
* Refugee (if the exile is fleeing persecution or war)
* Fugitive (if the exile is fleeing from the law)
More poetic/literary:
* Wanderer
* Sojourner
* Nomad
* Displaced person
* Stranger in a strange land
The best term to use depends on the specific situation and the desired effect.