I just installed my first forum using SMF (Simple Machines Forum). I'm a big fan of vBulletain, and did not want to use anything else, but I wasn't going to pay the exorbitant license fees. I read a recommendation here on BHW for SMF, checked it out and found out:
1) It's open source, which is really good in the Mozilla/Firefox sense of the word. Lots of Mods, and you can create your own if you have the skills.
2) I've installed enough Mods now to believe that anything I might want, I can find. YouTube Mod allows embedded YouTube videos, numerous anti-spam Mods, etc... So far, I haven't needed anything I haven't found.
3) Reasonably good support forum. They are big believers in RTFM and not so much befriending newbs. Not overly friendly, but the information is there if you are willing to both ask for it and dig around a bit.
4) Installed extremely easily. BlueHost's cPanel has a premade installer for SMF, so I only had to push a few buttons and made ZERO decisions and it had the forum installed in about 15 seconds.
5) Has an Ad-Sense Mod. I've installed it, but haven't associated it with an account nor enabled it.
6) Has a Google Analytics Mod, which is working just fine.
I could go on. If you are interested in seeing my SMF Forum in action, send me a PM or find me on Skype. I think I have a link to it in my profile also.