phpbb is probably the most popular one out there, and it's fairly good at what it does. However, because it's so popular it's a prime target for hackers, exploiters, etc. You really need to stay on top of updates and patches, because the minute slip on those, you'll discover your forums have been hacked. I don't know what it does for spam, though.
My forums are currently offline, but I run them through Drupal (similar to how these forums are Wordpress-based). I control spam by using the Mollom plugin.
MyBB is something I looked hard at once upon a time, but it didn't have all the features I wanted at the time. It looks like it's come a long way since then. Here's a review: http://www.forum-software.org/mybb/review