http://login.salesforce.com/help/doc/en/sites_limits.htm

There are limitations on bandwidth and processing time. Has anyone run up against these limits? How do people mitigate the likelihood of those happening?

For the bandwidth limits, I suppose you could host images and other static (non JS of course) files, especially larger files, on a non Salesforce server. While possible, it is not ideal because then you have to pay/maintain for something else. Salesforce is no longer the one-stop shop. (If it isn't in Salesforce it doesn't exist, right?)

For the processing, caching can be used in some cicrumstances, but what if the pages are very dynamic in nature and involve a lot of user interaction? I don't want to prematurely optimize (it's the root of all evil, after all).

While I do my best to avoid hitting them, these types of Salesforce limits that affect public facing websites keep me up at night. ;)