The fanciest shops. Sometimes these places have good closeout or clearance deals, but mostly I use these sites to get more detailed information about products.
There are a host of other online bike shops that are similar to these in their product offerings and prices, but these are a good representation of the category.
The ole standbys. Performance Bicycle Ship and Bike Nashbar are old mail order catalogs that have been around for ages. Their pricing is often discounted, and they very often have 10 and 15 percent off sales (occasionally a 20% sale), and they have store brand stuff that is cheaper. A word to the fashion conscious: Performance and Nashbar branded stuff is kind of ghetto. You can get away with Performance kneewarmers here and a Nashbar skullcap there, but outfitting yourself entirely in this stuff would be a fashion no-no.
Performance and Nashbar are good places to find commuter-style gear and entry-level stuff, but bad places to look for the high-end. Also, Performance has actual bricks-and-mortar stores in PA, so you'll pay sales tax for your orders.
The discount sites.
eBikeStop.com. Often has the absolute lowest price on components. Plus, price matching.
Price Point. Same deal as above, minus the price matching. More mountain bike stuff on this site.
Sierra Trading Post. I love this site. They by no means have a comprehensive selection of gear. In fact, it's usually old model year or discontinued items...and often you'll order something and find that it just doesn't work...but they have an awesome return policy, so there's no risk. The thing with STP, however, is that the stuff they do have is marked way, way down...and they are constantly having promotions which takes an additional 10-30 percent off. A great place to look for performance clothing and outerwear.
backcountry.com. At the outlet site (there is both the normal backcountry.com and the backcountry.com outlet) it's sort of the same deal as with Sierra Trading Post. The deals are not quite as spectacular, but still pretty good.
backcountry.com also runs several "one-deal-at-a-time" sites. The bicycle related ones are bonktown and chainlove.
Other places. Don't be afraid to shop eBay for goodies as well. If you're tentative about bidding, there are plenty of folks running eBay stores that have great deals on all kinds of stuff. When I buy things like chains and cassettes it's usually from an eBay store.
I also really like google shopping. Google whatever product you want. Then at the top of your results page you'll see a link to "shopping." Click on that and you'll be introduced to about a bazillion online bicycle shops. Careful, though, often the prices that appear lowest are prices in Euros or Pounds, and after converting your currency, taking into account the conversion fee your credit card company will charge you for ordering from the site, and the added shipping expense, it's not as good a deal as it appears. Sometimes, however, products are much cheaper in Europe than they are in the US (things like Victorria tires), so it is worth it to buy from a European site.