Even though I'm in my first week of law school and probably should be using this time to study torts and contracts, I feel I can add to this. Currently, you can fly from HPN to ORD on either United or American (737-300/500 or F100s) to DTW on Northwest (either Dc-9s or Avros) to IAD on ACA (J-41s) to CVG on Comair (CRJ) to PIT on USAirways (F100 or DC-9, possibly 737s) and to a variety of Northeast destinations on USAirways Express or Business Express.
The reason more destinations are not served from HPN is complicated. First, the residents of Westchester County (of which I am a resident, when not at school) do not want it to be a major airport, because of noise and environmental concerns. Second, the airport makes it very difficult for the airlines to work there. For example, the airport has two jetways, but the management does not assign them on a regualr basis and restricts their use as a ways to get back at airlines for various infractions (most likely noise related -- VERY strict noise abatement rules in place). Also, there is limited ramp space at the terminal and little extra room in the terminal. At the end of the 80s, Westchester voters barely passed a referendum to build a new terminal (the old one was a WWII vintage hut), but as part of the agreement, forced the County to build it very small, with little room to expand. It also only has one runway long enough to handle commercial traffic because of two trees that block the approach to the intersecting runway. These trees are located in Greenwich, CT and therefore, Westchester County, in NY cannot touch them (this is big issue). For these reasons, among others, traffic cannot expand to the airport.
Although it does primarily serve Westchester County, it is a good option for people from Manhattan because, when accounting for traffic, it takes about the same amount to reach as JFK and not much more time than LGA. I fly out of there several times a year to get to school and have connected through ORD, DTW and CVG to get to SBN. For those in Westchester, HPN is very convenient.