I'm from CT originally, live in VT now, but Albany, NY is where home is for me. I graduated from college there this past May, and moved up to VT for work with my girlfriend. Whenever we go back down for a weekend to visit, these two places are always at the top of the list:
Mahar's- Corner of North Allen and Madison. Constantly rotating selection of 30 or so beers on tap, 5-10 cask ales, and upwards of a hundred bottled brews. There's a computer in the back where you print out the menu, and it assigns you a number. When you order, the bartender checks off each beer, and the next time you print it out the one's you've ordered already won't be there. That way, you have to try something new each time you go. You get a t-shirt at 50, an engraved mug at 125, and a case of your choosing at 200. By far my favorite bar in the world.
Wolff's- A very very close second. Way downtown on Broadway, in the warehouse district. 30 or so draft and bottled beers, exclusively from Germany, Austria, Belgium, and the Czech Republic, with a kickass menu of traditional German bar food (various handmade sausages, potato pancakes, sauerkraut, German potato salad, and daily specials). Long, unfinished wooden picnic tables and peanut shells everywhere. Cash only, and beer is served in .3, .5, and full liter mugs.