How many redirects are too many redirects?

Heh. This is certainly a question that experience answers. I've worked with many sites and oh-so-many redirect issues. It doesn't take years of experience, however, to spot the killer redirect scenario -- infinite redirects!
Whenever sites start chaining redirects together there is a risk, often a small one, that redirects might start pointing elsewhere in the redirect chain. Search engines really dislike that. It's a very bad experience for the users too. What's more; with the now rapid advance of mobile search these redirects look like a slow mobile download and keep users waiting and frustrated. The iphone copes relatively well with redirect loops but some other smart phones do not.