http://www.invisionboard.com/
I use this board on my site... you will need hosting for it!
It will need PHP + MySQL.
I host my forum on my Linux box via my Cable Modem.... I purchased the domain stusplace.co.uk and just point it to my IP addy.
I don't think you will find something "free" that will host this board and it's MySQL database TBH.
You are probably better off looking for a site which lets you use their boards and suffer a banner add. At least banner adds don't open a shed load of browsers.
[Edit] IPB will host your board for you, at a cost...
Price (per/mo) $10.00
Setup Fee * $10.00
Data Storage & Usage
Bandwidth 10 GB
File Storage 50 MB
They are the "Basic" prices, more money gets you more bandwidth / storage.
Having said that, $10 per month is pretty expensive for what you are getting.