I've only needed root for two things - for the Android Market (despite the presence of alternative markets, the convenience of using the real Android Market app is really great) and to install the google calendar sync adapter so that I can use the pocket informant app (that I got as a free app of the day) or the google calendar app with my google calendar.
For most people, really not necessary.
From the Android Market I've gotten a few good and useful apps that aren't in Amazon's market: Battery Monitor Widget (highly recommended if you want to understand your Fire's power usage), Disk Usage, Dropbox, Ghost Commander, Mobo Player, Opera Mobile, QuickPic, Titanium Backup. I'm sure I could have gotten them from elsewhere but the market app makes it easy to find them, get them and update them.
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