Got my rejection from the Lower Manhattan Cultural Center's studio program this weekend. I think they take applications twice a year. This is a studio program only, the same one that previously had studio space in the World Trade Center.
Here's a great source for those interested in pursuing a full residency, The Alliance of Artists Communities. I have multiple rejections from many of these programs, and some are much more competitive than others.
The Vermont Studio Center is an excellent residency program, and you have a better chance of acceptance by submitting to the Vermont Studio Center, because this is a year-round program, as opposed to something like Skowhegan, which holds only one summer session each year.
All of these programs have different missions, merits, and reputations. A residency at Skowhegan is, rightly or wrongly, considered a better "get" than one at the Vermont Studio Center. Both offer relatively the same thing, but because VSC operates year-round it can serve ten times the number of artists who are able to attend Skowhegan, and Skowhegan consequently is regarded as the more competitive and intense session. I know one guy who went to Skowhegan after VSC and when he said to his Skowhegan friends he was looking forward to going back to VSC someday was told "you can't go back". I've got three Skowhegan rejections so can't report first-hand, but from what I understand it is on average a much younger, intense, ambitious, and competitive crowd than you will meet at VSC.