Pros: Tons of snow, late spring skiing, most extreme terrain east of the Mississippi
Cons: no amenities whatsoever
Because of its location and the prevailing winds, Tuckerman's collects huge amounts of snow, typically 50 feet or more at the base of the bowl. This is both a plus and a minus. It's a plus because there is still skiable snow at Tuck's long after the rest of the East is done for the season. Typically, the most popular time to ski Tuckerman's is late April into early May, although Tuck's can frequently be skied into June. The downside to all this snow is avalanche. Tuckerman's is extremely dangerous in the winter due to avalanche, and was closed off by the Forest Service in the past. Now it is accessible year round, but it is still considered a very bad idea to ski before late March.
As if skiing Tuckerman's wasn't hard enough, just getting to Tuck's is a hard slog to start with. There is no transportation up to Tuck's except your own two feet. You start at the Pinkham Notch visitor's center on Route 16. From there, it's about a 2 1/2-3/12 hour hike, where you gain about 3000 vertical feet. Then you get to Hermit Lake (HoJo's), where the campsites are. From there, it's another 45 minute hike to the base of the bowl, and then it usually takes about 30 minutes to hike up the headwall. If you're there earlier in the season, you'll be able to ski back down the Sherburne, but they will start to close that as the snow cover breaks up.
If you want to ski Tuck's, your best bet is to camp there. There are a number of lean-to's there, maintained by the Appalachian Mountain Club (AMC). You have to get your camping permit the day you plan to camp, and there are only 86 spots at the campsite. So people get there to line up before the Visitor's Center opens, which is at 6:30AM. Since there are lean-to's, you typically don't need a tent. But all the other camping gear is a must, especially a good sleeping bag, since it can get very cold at night. You have to pack in your own food, and there is no clean water source. The Cutler River headwater is nearby, so you can filter or treat water from that.
Despite all the difficulties, Tuckerman's is a phenomenal experience. Skiing down the headwall is such a huge rush, and having gone through such a hike to get there, it's something you really feel like you've earned. The overall atmosphere is a lot of fun, essentially a big end-of-season party. There people hang out at Lunch Rocks between runs, and cheer for the good runs, and heckle the crashes (of which there are many). If you live in the East, and you can handle it, Tuckerman's isn't something to be missed.