Great news for Droid 3 users! The root for this Android monster by Motorola is out. Steps are similar like any other Android rooting, so you shouldn’t have any problem if you have done so before. Folks at Rootz Wiki have created this utility which will root Droid 3 in a click. At the end note, follow these steps to root your device in a simple and easy way.
1. Install Motorola drivers
2. Download and unzip Droid 3 Easy Root Script v5 (to download)
3. Enable USB Debugging by navigating to Settings > Applications > Development > USB Debugging.
4. Connect device to computer and select Charge Only mode.
5. Locate unzipped package from desktop and double click Click To Root Your Droid 3.bat.
6. Follow step by step instructions and … ‘done’.
Download rooted apps and see if they work out for you. If they do (which should be the case), you have successfully rooted your device.
source: Rootz Wiki