Priceline
A great, straightforward and simple introduction to successful Priceline bidding is this 2003 article from the Washington Post by Michael Shapiro.
About.com has a good, clear explanation of how free re-bids work. That's probably the single most important 'trick' to learn.
The best uber resource for informed Priceline bidding is Bidding For Travel.com. Some users are unhappy with the level of moderation there, but it is indispensable for the lists of hotels by zone and quality level and the tremendous amount of successful and unsuccessful bids that have been posted. Their Hotel FAQ is also important reading to understand how to get the hotel(s) you want in the right location and at the best price. Furthermore, their discussion boards contain really interesting tips such as advanced rebidding techniques that increase your free re-bids beyond those conventionally recognized.
An alternative to Biddingfortravel.com is BetterBidding.com which is newer and not quite as extensive. It does cover Hotwire as well as Priceline, so adds some unique value (see below).
How to earn miles for your Priceline booking: If you bid through eBay's travel portal, you earn 1500 eBay Anything Points. This FatWallet Thread shows that through June 30, 2004 you can convert those points into just over 1500 American Airlines miles -- three times as many miles as most hotels award on traditional bookings.
Hotwire
- Hotwire doesn't seem to provide deals quite as good as Priceline, at least in my experience. That's probably because hotels set rates they offer Hotwire and then Hotwire offers those hotels plus a markup. Their markup is greater than Priceline's booking fee. However, it's a good idea to check what's available on Hotwire before bidding on Priceline (so you don't overbid) and because you can figure out what hotels specifically are on offer in many cases easier than with Priceline, especially if you check BetterBidding.com which maintains Hotwire hotel lists. (Hotwire lists a quality level and amenities for each property which can be used to decipher that hotel's identity.)
Traditional Booking Methods
SideStep is a downloadable tool which detects when you're on a travel site and takes the information you've entered, sends it out to different hotel search engines, and brings back prices. It's a great quick way to compare options.
TravelAxe is another downloadable tool, much more powerful than SideStep. It's probably the ultimate hotel booking device -- it goes out to the different travel portals, pulls results for a huge number of hotels, and shows a comparison of rates in a simple grid. Indispensable.
Hotel Reservation Service often offers the best price on rooms.
QuickBook is a consolidator which is useful in some cities, often beating the best price elsewhere.
Once you've settled on a hotel, check the rate on the hotel's website. Many chains don't give points or frequent guest benefits to people who book through other channels, so if the price is the same book through the hotel directly. If the hotel's price is higher, check out their website's "Best Rate Guarantee" -- someone (maybe I'll add this later) needs to write a FAQ on hotel best rate guarantees because some are easy to work with and others are sketchy. But they all hold out the promise both of matching rates and giving you something extra.
How to Decide Which Hotel to Book
Obviously there's proximity to events or attractions you're planning. And there are features or amenities offered by the property.
Don't believe 'star ratings' or at least recognize that some ratings are more reliable than others. Hotels.com used to allow properties to "self rate" meaning that a hotel would decide how many stars it got! Now they at least do some checking and independent verification. Expedia's star ratings are notoriously unreliable. AAA and Mobil guides are far better, but even there the guides don't visit each property regularly.
When considering a property, search for reviews. TripAdvisor.com is a good source of hotel reviews. Just recognize that different people have different experiences and standards, so they may be set off by things that wouldn't bother you one bit. For instance, resorts have expensive food. Pretend you're eating out at a nice restaurant in Manhattan at every meal. For folks who don't expect that, they're likely to write a negative review. The best approach is to read alot of reviews and look for common themes across several writeups.
BetterBidding has hotel reviews and so does Epinions and Biddingfortravel.com.
Miscellaneous
You can always get free lodging by sleeping in the airport.
Make sure that when you've booked a room through a conventional channel, that you join that hotel chain's loyalty program. First you'll earn points (towards hotel stays) or miles in your favorite airline program. Plus members of a hotel's loyalty program often get preferred treatment such as room upgrades.
Check out Webflyer's searchable database of hotel bonus promotions some of which require advanced registration. No reason to miss out on bonus points for a stay you're already making!
I'd love comments/feedback/additions/modifications! Let 'er rip! 
