Both my brother and I have had iPhones for a while now, and although webapps are nice there have not been too many show stoppers. In fact, I only have a few web icons installed; however, Springlets is a true show stopper.
"Springlets are tiny apps for your iPhones Home screen that help you save time."
There are several different search springlets including imdb and wikipeida ones (which saves a lot of time by just popping up a search box instead of loading the whole page), but the Springlet I like most is the speed dial one. Simply enter in the person's name and number, pick the color icon you would and you're ready to roll.
To check out all the different Springlets visit www.springlets.com on your iPhone.