vBulletin was the early king of this stuff.  However, it started having major spam and graphics issues later on down the line.  Nonetheless, I'm not sure if it was due to the software - or the forum owners.

Now, looking at XenForo, Invision Power Boards (IPB), and Burning Boards, I can't really decide which is better - cause I'm only familiar with XenForo from the admin POV.  Can anyone give me some thoughts?  OK, I can say that Burning Boards is the cheapest - but that may not mean it's the better deal.