This is a very interesting question. :01:
Caching can mean a lot of thing. There are many many implementations and approaches.
For example, if the site is using mysql query caching, this is based on size, so a possible way to bypass it is to request for pages that have not been recently viewed, thus (given there are a lot of pages) overflowing the cache size and throwing the cached results of the target page out of it. :hump:
If the site is using page cache, based on time expiration - you probably can't do anything. This can be either to internal implementation (see some WP caching plugins) or due to an external proxy (like Squid). The trick hostwinds mentioned would fall in this category and I was not ware of its existence. If the domain is not on a dedicated ip though, it will probably fail as the web server will probably deliver a test page or a random domain hosted on that ip.
If the site is using object cache, depending on the implementation, it probably has either size or time limits. So, the overflowing method might work again.