Well I have pretty extensive experience in the following:
phpbb (2 and 3)
SMF (1.x series)
vBulletin (3.x series)
IPB (3.x series)
and my latest venture is MyBB.

I chose MyBB because I was using IPB and I got tired of the $25 renewal fee every few months, MyBB seemed like the logical choice because the MyBB software is very similar to IPB in a lot of aspects.

My favorite? I suppose whatever software I am on at the moment is my favorite, otherwise I wouldnt be using it right?
Like if you asked me a couple years ago I might of said phpbb or vBulletin but if you asked me today, I'd say MyBB