I have only used Priceline in the past for hotel rooms.. and only for short stays (1-2 nights). That's pretty safe compared to Priceline Air tickets, where departure/arrival times can vary wildly. In terms of pricing, I only bid amounts that are lower than whatever hotel sites have.. in the past, I've gotten a Sheraton LAX room for $45 and a Holiday Inn Select for $36 (all fees/taxes included).

Most hotels will never go < $50/night, so sometimes the savings is well worth the lack of FF points. Oh, and yes.. I always give them my number, just in case it's a trainee.