We've had people in large-scale publications as well as national televised programs and national news.
Its really a crap shoot because you can never tell. It usually is not as big a problem as one would think. But I have seen it go both ways.
How we handle it is offer them a dedicated server for the month at the regular rate of the dedicated server, which is like $300 or so. That gives them 2000 gigs of transfer "padding" Then they still have the choice to stay on the shared server if they want to gamble on it, then they can upgrade to other hosting plans as they need it.
We have also been known to exchange some exposure on the featured site in trade for a reduced rate on the fees we would normally charge. Depends on what it is, and how popular we think the click though rates to our site will be from the featured site. that does not happen for everyone though, but for some, we are willing to help share the expense in exchange for some extra exposure.
After 100 gigs of usage (Reseller Elite) then it runs $1.00/gb "on demand"
We have to charge it that way because its similar to how we are charged. If we have time to arrange a dedciated server for them ahead of time, then we have some padding on the transfer fees from the datacenter. But if their site is on the shared machine and it causes us to exceed a certain limit, we get hit with overages and have to bill for it.
Generally in the middle of a huge traffic spike its not convenient to transfer a site at the last minute to a dedicated server, not if you want it to be transparent to the site visitors. Its best to plan a few days ahead for that sort of thing. (if not more)