I know the former lead developer of SMF, so I may be biased.
SMF home page:
http://www.simplemachines.org/
The SMF community forum:
http://www.simplemachines.org/community/index.php
To see large installations in action:
http://rankings.big-boards.com/?filter=SMF,all
Security info:
SMF:
http://secunia.com/product/5285/
PhpBB:
http://secunia.com/product/463/
vBulletin:
http://secunia.com/product/3212/
Invision:
http://secunia.com/product/3705/
Nek or aetherFox can tell you what it's like to administrate SMF (they're the admins at
basicnetwork.net)
I can tell you [Unknown] prides himself on security and optimization. He was always writing converters (to convert existing forums to SMF), and in the process he'd be looking at the other forum's code and pointing out security holes
. Sometimes people would ask how many servers the SMF community forum was running on, and he loved how surprised they'd be when he said just one - an old Celeron with (I think it was) 256 or 512 MB of ram (they've since upgraded).
It's free (as in zero dollars - you get the source code and it's readable and well commented, but it's not GPL and you can't redistribute), can do far more than phpBB, and has a much better security record. Plus it's well optimized - it runs with lower load averages than other forums with as many features/as much traffic and has lower hardware requirements.
As far as I know, all the other forums in the same class (for features) are slower and cost money. Like
Invision and
vBulletin.
For best results (with any forum), use with eAccelerator:
http://eaccelerator.net/HomeUk
Basically, everytime apache runs a php script, it's recompiling it every time. eAccelerator caches the compiled byte code. It's under the GPL.