A bit of explanation about Boston's climate: One might think that Boston would have a temperate climate because it is by the ocean, but no. Boston has an unfortunate climate because the winds are west-east rather than east-west. This makes it so that we get all the wonderful leftover extreme, uncalmed-by-ocean weather from mainland America rather than the mild, ocean-scented weather of a much more beautiful place like Santa Monica.
Summary of year-round weather: To properly deal with the winter, it is extremely important to invest in at least one good coat and one good fleece. The weather goes something like this: the summers are nice, averaging mid-80's and varying a lot. The fall is beautiful, usually involving a long Indian summer extending into October, a phenomenon that tricks you into believing that perhaps winter will not come. LIES. The cool late fall begins creeping in late October/November. December is when the colder cold begins to hit and people begin to expect snow. At this point the temperatures are probably in the 30's and 40's. The coldest cold comes at the end of January, when it is not surprising to have at least a week in the high teens and low 20's. Winter takes a long time to leave: in early March you might see temperatures in the 50's and 60's, but these usually happen for no more than a couple of days at the time. In April and May there is a lot of rain and short lengths of good days. It is not really consistently nice again until June, where the temperature is in the 70's and 80's and it is nice except for when it rains.
The year in clothing: in the summer it is good to have a light jacket or two and a raincoat. There are intense thunderstorms with extreme winds, so you probably want to invest in a sturdy umbrella as well. It is good to have rain boots all year round. A heavy pair of winter boots is also an excellent investment, especially if you plan to walk around. I recommend having a fleece/wind-proof fleece for the fall and as a general layering tool. A good down jacket is an excellent investment, but it is also important to have something wind-resistant to put over it, as Boston is one of the windiest cities in the US. (Wind makes cold feel much colder!) As for my coats, I have a wind-blocking fleece (North Face WindWall) that I wear in the spring/fall, a heavier fleece (North Face Denali), an extremely warm down jacket, and a two-piece jacket involving a windproof Gortex outer shell and a zip-in down inner thing (North Face Triclimate). I also have various pea coats and other things that look nicer but keep me less warm.
Non-coat cold protection: Very important! Get a good hat and gloves. A scarf also helps a bunch. Layering under coats is also extremely important! Long underwear is a good idea. On very cold days I wear long underwear under my pants, but my roommate Aliza and I are the only people I know who are really into this. Fleece pullovers are also a great layering tool.
Running outside: You might also be wondering about what to wear if you are a runner and don't mind inclement weather. In the winter I usually run in spandex leggings, a turtleneck, and maybe a wind-blocking jacket/pullover. I also have a pair of not-great running gloves and a hat. (My roommate Brigit, who has better gear in general, has an amazing pair of wind-proof running gloves of the kind that I am too cheap to buy.) This tends to keep me warm enough. When I used to run outside when it was in the 20's I used to layer long underwear under a pair of wind-blocking pants, but I have since renounced such acts of extreme masochism.
WARNING: If you are moving to Boston, MAKE SURE YOU HAVE WARM CLOTHES NOW! I recommend looking online for good deals on high-quality jackets, since when it comes to protection against the cold, quality (and quantity) make quite a difference. I get a lot of my weather-protection gear at Eastern Mountain Sports.
Boston's redeeming qualities: Why live in Boston then, you might ask. Most of the reasons are unrelated to weather. There are a few weather-related reasons: the summers are beautiful, the extreme weather makes the sky really beautiful much of the time, and there is really good snow for people who are into that kind of thing.
Note: Clearly Boston has a few redeeming qualities, as I am staying here indefinitely for graduate school after suffering through four years of awful weather and consequent infirmities as an undergraduate.