There are many advantages. Ill start with the few disadvantages since jesse got most of the advantages.
Verizon- tech support is just about useless in most cases, but then again if you're good with making sure you have good backups, you won't need em. Also, no warranty replacement unless you return your phone to stock. But then again, if its ok now... it'll probly be ok till you get rid of it.
Things go wrong- it can be a scary thing with rooting and flashing roms. You can cause alota grief for yourself, in extreme cases ruin your phone till you fix it with a computer. Then again when I light a cigarette, I can light my head on fire. But it doesn't stop me from smoking, just makes me watch what I'm doing... and as long you're careful with your backups, you'll be ok
Now advantages
Tethering w/o big reds big charge
Removing bloatware like amazon mp3 store & such
Being able to move whatever apps I want to SD
Overclocking from stock 600mhz to 1ghz made it feel like a brand new phone. All the new apps these days are taylored to phones with 1ghz cpus anyway, its the new phone standard these days. Not all droids can go that high, but most can I believe.
A huge thing is being able to flash roms & backup! Nandroid (used thru rom manager) will allow you to easily allow you to backup/restore whatever roms you use. Finding the right rom for you is different for everyone, and the customizations from all the ones out there are amazing!
Now apps
Rom manager- switch roms easily, backup, restore... simply awesome.
Titanium backup- move whatever you want to SD, backup your apps so you don't have to redownload them when you start flashin roms
Setcpu- your overclocking needs are solved. Plus, you can have it change how fast your phone is (or battery saving) automatically based on phone temp & battery among other things.
There's more, that's just the basics. Once you get the hang of a rooted lifestyle, you'll kno what else you'll need
Root, you won't look back. but you can if you wanna... but why would you wanna do that? Hope this helps a bit