Over at Baseball Savant, Daren Willman has put together a neat interactive chart that lets you explore how far each team will travel on the road in 2014. The Mariners—who are around 700 miles away from any other baseball team—will travel the farthest total distance at 51,540 miles. That's more than double the circumference of the Earth (24,902 miles)*, and 2.2 times farther than the geographically-centered Cubs will have to travel (22,969 miles).
In case you were wondering, yes, the Dodgers/Diamondbacks trip to Australia is included:
*At the equator, you ridiculous pedant.