General:
* Traveler
* Wanderer
* Pilgrim
* Sojourner
* Journeyer
More specific:
* Foot traveler: Pedestrian, hiker, trekker
* Long-distance traveler: Adventurer, explorer
* Religious traveler: Pilgrim, devotee
* Someone who travels by chance or fate: Drifter, vagrant, nomad
The best synonym depends on the context. For example, if you're writing about someone who is traveling for religious purposes, "pilgrim" would be the most appropriate. If you're writing about someone who is traveling for pleasure, "traveler" or "journeyer" might be better.