Amazon has released Price Check, a free app that allows you to do some comparison shopping. You start by saying the name of your target product, scanning its barcode, typing its name, or snapping a photo. You'll get several results; tap one to see who's offering it with prices and shipping costs listed. Of course, Amazon hopes it has the lowest price, but it doesn't always win.
I tried the app in a local store and found the barcode scanning and voice recognition worked well. I took a picture of some DVDs, and the app figured out what the movie was and offered meaningful price comparisons to other retailers.
I used to use the Amazon Mobile app in bookstores while I browsed, and I often just ordered from Amazon while I was in a brick and mortar book store. I felt bad, but sometimes the price differential was too significant to resist. You can share your pricing info via email, text message, Facebook, or Twitter. The Price Check app is listed for the iPhone only, but it will run on the iPad and the iPod touch. Amazon also has an iPad app called Windowshop, but it doesn't do price comparisons and is just an easy way to shop at Amazon.
Price Check is so good that I can't conceive of shopping without it. If you want to give it a go, be careful -- there are a bunch of apps with Price Check as part of the name. Price Check requires iOS 3.1 or later.