Well the 'best' solution would be a large server farm that pays for itself....one can dream.
We run a dedicated box for two forums at the moment...no way we could do this with shared hosting. Neither forum is considered a "big board" although given another year one of them will probably be there stat wise. Regardless we have our share of server problems due to the load because one of the forums has an
very active "turbo posting" user base. They also have a few modifications installed that I could personally do without (I yanked their shout box ages ago

).
As you can see our main problem is concurrent users (as Marco pointed out in his post above). We aren't to the point where we need new hardware yet..but it'll be soon if we don't get our server loads down.