The biggest YaBB forum I've come across is one that is based here in Russia. The last time I checked, the following is what I read:

Statistics for: Absolut Games
Russian video gaming discussion board
http://forums.ag.ru/

Forum software: YaBB
Number of posts: 6144156
Number of members: 464120
Post per member ratio: 13
Posts last week: 7359
Alexa ranking: 1868

The 2nd biggest YaBB forum I've come across is one that is based here in Germany. The last time I checked, the following is what I read:

Forum software: YaBB
Number of posts: 1263421
Number of members: 14526
Post per member ratio: 87
Posts last week: 0
Alexa ranking: 614500

On the note about a forum being the "biggest" as it were, I think the number of registered members is far less relevant than the number of posts.

Or maybe most relevant of all is how often any given forum is updated. Certainly to those members, even if there are only a handful, a regularly updated forum will be very relevant.

www.silenthill-forum.de still active (for nearly 8 years now)  

Hehe, yeah. I've installed so many mods and changed so many things by my own that you could call it something like an inofficial YaBB 1.5 

And what shall I say - this YaBB runs for over 8 years now, on 3 different servers and 2 different web hosters, and we never lost any data. It works and works and works.

The LaserPointer Forum used to be on YaBB before problems kicked in because of his large member base.

The problem was that he had over hundred users all at once access and posting at the same time. The ISP sold him phpBB on an enterprise MySQL system (Yuck!)

This was a system issues and not a YaBB Issue. In testing it with a SSD (Solid State Drive), I found that YaBB can easily handle a couple of thousand users all at the same time.

Back then, The Laserpointer Forum has about 17,000 members, when about 100 - 250 users and a couple of thousand guests trying to access it.  Now it has 25,000 members with about 300 - 500 users and 4000 guests accessing it. You consider the size of that and YaBB being able to hold on its own on a cheap isp set up vs. phpBB on an enterprise set up, YaBB is the better of the two.