The per-person cost, amenities, and proximity to the slopes can all affect lodging decisions. In general, expect to pay extra for greater convenience, privacy, and luxury, and try to reserve as soon as you know your travel dates. Accommodations for the busiest parts of the season book up early, though you may be able to be spontaneous in the very early or late season.
Hotels. A hotel right on the slopes is very convenient, but may be the most expensive option. Hotels and motels farther away from the resort often cost less, but you'll have to drive or catch a shuttle to the ski area. Hotels have maid service, and many offer gyms, Jacuzzis, bars, and other diversions. However, per-person costs can be high for a family or group, and you'll have to take all your meals in restaurants.
Rentals. Resort areas are full of condos and cabins you can rent for a weekend or the whole season (if you ski a lot). Mostly, these are the vacation houses of private parties who rent them out when they're not using them. If you're traveling with a group, a rental can be very cost-effective: Per-person costs are lower, and cooking in the kitchen helps keep food costs down, too. You do have to clean up after yourself, though.
You can find rentals through ski tour operators or specialty realtors in the area you plan to visit. Use the area's yellow pages or type "vacation rentals" and the name of the town or resort into an Internet search engine.
Other options. Bed and breakfasts may be available, and tend to be cozier and homier than hotels (although just as expensive). Hostels offer no-frills dormitory beds (and some private double rooms) for rock-bottom prices--and they may have a communal kitchen you can use, too.