By car
I-90 also called the Massachusetts Turnpike, or simply the Mass Pike is the major East-West route across the state. Rt 2 is a more northern equivalent, though there are sections through town centers with traffic lights.
By bus
Peter Pan (http://www.peterpanbus.com/) and Greyhound (http://www.greyhound.com/) runs buses to many towns in Massachusetts.
By bike
There are a number of "rail trails" - converted rail road lines - throughout the state that have been paved for pedestrian and bicycle travel. There are also designated "bikeways" along secondary roads. See: (http://www.massbike.org/b...)
By road
Although it is illegal to hitchhike on the highway itself, I-90 has a very good system of commercial rest stops placed conveniently every few miles. Hitching a ride from these rest stops isn't too hard. Make a sign, stand in the parking lot and put out your thumb for cars on the way out. As these rest stops are quasi-private property, it may be advisable to buy something small, like a pack of gum, so that you are a paying customer.
On foot
A portion of the Appalachian Trail runs through the state.