What's Rooting?
---see: here or here
Benefits of Rooting:
---save applications to your SD card
---move caches to SD card
---remove unwanted applications
---flash custom ROMs (possibly with HTC Sense or MotoBlur)
---possibility to install a full Linux distro, i.e. Debian
---tether via 3G/WiFi without using 3rd party applications (PDAnet)
---get multi-touch everywhere (and pinch-and-zoom)
---overclock/underclock your processor (but overclocking can be dangerous)
---customize your bootup splash screen
---change your phones theme (colors and look, etc)
(Some of the benefits aren't simply automatic. For example, to save applications to your SD card, you need to "unlock" it by going through a documented process. Having your phone rooted will give you the "permission" on your phone to do this process.)
Dangers of Rooting:
---if the rooting process is done wrong (by YOU), it can 'brick' your phone (i.e. you have a VERY expensive, shiny paperweight)
---if you have flashed a custom ROM, you will no longer able to receive the automatic OTA updates (but the ROM creator should supply you with updates)
---voided warranty
Links:
---Droid Rooting Wiki (A (non-AF-supported) donation fund has been established here with the intention of whoever figures out how to root the Droid first will receive all of the donations)
---AllDroid.org Droid Development (Threads regarding development topics such as attempted exploits for rooting the Droid, Droid system dump, etc.)