I don't have any premium member programs set up. I don't even know what I would be able to offer anyone at this time. I have given a quick thought to possibly doing ad-free for members, but I don't have much in the way of ads, and it wouldn't be cheap in the long run.
Depends on the forum. Promotion forums are easier, allow them to have a sticky thread in the promotion board, discounts on services, double forum cash etc. It is harder for other niche forums, but a premium username colour and title, exclusive forum, bigger PM space and ad free etc usually work well.
Yeah we have founder perks. Xenforo doesn't allow for the same options as vBulletin, so PM inbox increase and larger avatars aren't possible ATM. We've given the people who donated in the 3 month fundraiser tiered status that come with a rank. Bronze, Silver, Gold and platinum founder. Also access to premium forums.
Not so much a premium perk, but if someone makes a decent post on the forum, such as a review or article, we throw the link up on Facebook and Twitter to give it more attention.
I currently offer them a free email address with a domain that is closely near the website's, having a custom badge, private forum to discuss and share possible ebooks and newsletters behind the scenes, and some more focused updates on adding more features to their usergroup/access.