If your page does five 301 redirects to get to the final page I'm guessing that google bot will follow it all the way there. However, there must be a limit at which point google bot says "hey, that's enough, I'm not going any further." What is that limit?
They recommend no more than 5, although they don't specifically say they won't follow more than that. Plus, if it's a lot, it will hit your page load time, which will have a seriously negative impact on your SEO.
Quentin, Vancouver: How many chained 301 redirects does Google not "like"?
Nathan J: It's ok to chain a few together; I would avoid doing a whole bunch, like 20 or 30. :)
JohnMu: As far as I know, the HTTP 1.0 standard allows for a maximum of 5 redirects for a URL. That said, search engines might treat it in different ways, so I'd recommend reducing the redirects to a minimal number.