I dunno if I'd call MA unique... just bizarre. We're probably bizarre in ways many other states are bizarre. It's just that we have an interesting combination of bizarrities.
At any rate... I actually can't speak for Eastern MA, so this will be a Western MA perspective. (With a slant mostly on the Berkshires.) I was going to post a whole essay... then I just decided to use a few joke letters I have hanging around, with some occasional commentary. (Er, sorry, this is sorta long...)
You really know you live in Western Mass when:
1. Your idea of a traffic jam is ten cars waiting to pass a tractor on the highway. (Seriously, traffic problems are pretty rare, except for Main Street in Springfield, which currently sucks.)
2. "Vacation" means going to Burlington, VT. for the weekend.
3. You measure distance in hours.
4. You know several people who have hit moose more than once.
5. You often switch from "heat" to "A/C" in the same day.
6. You use a down comforter in the summer.
7. Your grandparents drive at 65 mph through 13 feet of snow during a raging blizzard, without flinching.
8. You see people wearing hunting clothes at social events.
9. You install security lights on your house and garage yet leave both unlocked. (Only true in the more rural parts of the area.)
10. You think of the major food groups as: deer meat, beer, fish, and berries.
11. You carry jumper cables & a battery charger in your car and everyone in your family knows how to use them.
12. There are 6 empty cars running in any parking lot at any given time. (Again, only true in the more rural parts of the area.)
13. You design your kid's Halloween costume to fit over a snowsuit.
14. Driving is better in the winter because the potholes are filled with snow.
15. You think sexy lingerie is tube socks and flannel pajamas.
16. You know all 4 seasons: Almost Winter, Winter, Still Winter, and Construction. (I love this one... it's so true!)
17. It takes you 3 hours to go to the store for one item even when you're in a rush because you have to stop and talk to everyone in town. (Greeting passer-by, bus drivers, clerks, etc. is pretty common... a custom which got me into a mildly embarrassing situation in NYC, but I digress. Door-passing is common too, and not limited by gender.)
You really know you live in the Berkshires when:
1. You actually know the proper places to yield at Park Square. (It's a rotary, for the sake of explanation. We have a LOT of rotaries here in MA. Not to mention mandatory double-lane changes and other oddities. Incidentally, as you might have guessed, Park Square is round.)
2. You can't look at a Norman Rockwell painting without feeling a sense of pride. (He wasn't born in the area, but he had a home in Stockbridge, and his official museum is there. We also can lay claim to Dr. Seuss being born in Springfield and Herman Melville's home Arrowhead in Pittsfield, among some others.)
5. You wouldn't jump in Silver Lake for a million dollars. (Also for the sake of explanation, Silver Lake is a lake in Pittsfield that was used as a toxic waste dumping ground by GE while the company had a base there. I happened to live a five minute walk away from it back then. Do you know how frustrating it is as a kid living five minutes away from a lake you can't play in?)
6. You have participated in the "Hometown America" parade. (One of the biggest 4th of July parades in the country, and probably the area's only claim to fame.)
7. You have at least 5 relatives that USED TO work for GE. (GE used to be Pittsfield's main employer. Now it's Lockheed Martin, IIRC. Yay.)
8. You know what PCB stands for, and know how many of them are in your backyard. (Again, thanks to GE's lousy waste-handling practices.)
9. You know that there is no logical explanation for the boat sticking out of the Allendale Shopping Center parking lot. (Another Pittsfield thing. Actually, the boat is now gone... now there's sheep statues all over downtown instead. Cheshire may have a statue of a cheese press in the middle of town, but at least they have a somewhat cool explanation for it.)
10. You curse the designers of the Berkshire Crossing parking lot. (Berkshire Crossing is a shopping complex in Pittsfield. Let's just say I think the parking lot designers were channeling M. C. Escher at the time.)
11. You talk like you're from Vermont. (I personally don't, but this is generally true. BTW, no, we don't talk like Bostonians.)
12. Most of the year you are surrounded by tourists.
13. You have had 3 or more consecutive snow days.
14. When someone asks, "Do you live near Boston?" you can't help but laugh. (I swear, everyone non-Western MA asks this. Either that, or they say they thought we were part of New York. Sigh.)
Other things not mentioned:
Collleges. Dunno if we're the state with the most colleges, but we have a crapload of them.
We are mostly religious. However, we are also mostly liberal. However, we still haven't repealed all our Blue Laws. Nobody really finds any of this odd, for the most part. (Our liberalness is the main reason why I'd have a hard time getting along anywhere else.)
I think this is a New England thing in general, but... we have a LOT of cities with Native American or British names. Also, many of them are not pronounced the way they're spelled.

There are several companies that either were founded, have their main headquarters, or both, here. Among them are Smith & Wesson, Staples, Big Y, and Friendly's.
Peace & Luv, Liz