Biggest diameter, not counting shotguns, would be a .585 Hubel express we built for a guy. I shot the barrelled action into the bullet trap without a stock, which might not count but was impressive, trust me. There's a video of two of the other guys doing it on youtube somewhere.
Biggest in terms of powder charge is the trusty .50 BMG.
In terms of "why the fuck would you ever want that" big guns I've fired, I think the 7.21 Lazzaroni Firebird takes the cake. It's not objectively large compared to most other stuff, but it's painfully overbore, and I'm not sure what a person does with a .284 diameter bullet going near 4000 feet per second.
There's one of these hanging in the storefront. It's a little broken and I maybe knocked a few parts off it when I was hanging up a zodiac next to it when I first started here. It's a pipe dream, but I'd love to somehow get it running again and shoot it some day.
http://www.ebaumsworld.com/videos/the-punt-gun/81579954/I mean come on, doesn't that look fun?