My oldest forum that I still own is 10 years old. The oldest that I used to own and sold is 20 years old and still going strong. I am actually thinking about buying it back from the current owner.
Nice question! Our webmaster forum http://www.webmastersun.com is about 3 years and growing...the reason to make it success is a good design with active members, new members and useful posts daily on the forum. It will make your forum always fresh and updated to visitors when viewing it.
I ran it for about 10 years and let it go... It was going okay. After four years I am attempting to try again. Not so easy this time around it's been maybe close to 12 months I think?
My forum is technically only 4 years old next month...However, I consider it a spiritual successor to the forumotion site we made in 2011, so I say it is nearly 5 years old(come this October) :p
One of mine is just over 10 years old. My original forum (in various incarnations) is 15 years old, using vBulletin, SMF, Mambo CMS, Joomla, Wordpress, and now XenForo.
My forum is just two years and its getting traffic and new registered user everyday and its also spam free.