Teamsters Local 25 - These guys drive and are responsible for all the vehicles used on set, including crew shuttle vans, "star cars" for celebrity actors, wardrobe trucks, catering trucks, grips trucks... the list goes on and on. They are local to Boston and northern New England. My experience, as a female, is that they're generally tough-guy-with-a-heart-of-gold types. My coworker, who is male, would like to add, "Don't ever fuck with the Teamsters."
IATSE Local 161 - These are your production office people: the Production Coordinator, APOC, the Accounting department, and Script Supervisor. This local is run out of New York, but covers the New England region.
IATSE Local 481 - This union represents a whole slew of departments, including (in no particular order) Art, Grips, Wardrobe, Electrics, Props, Special Effects, Set Dressing, Greens, Construction... I'm forgetting some here -- and I apologize. 481 covers New England, but not New York.
IATSE 600, International Cinematographers Guild - This is the Camera department's union. This is not a New England based local, so you'll run into 600 members in New York and beyond.
United Scenic Artists 829 - These are the artists who do everything from elaborate production designs to painting walls. You'll often see them covered in paint splatter... lovely people. The 829 covers New England, New York and beyond.
There's also SAG for actors, DGA for directors, WGA for writers, and the PGA for producers. These people are "above the line" and tend to get flown in from LA.