How many 301 redirects in a row can I use?

If possible: none at all. Why?

301-redirects take time and users are often impatient. Depending on the server load and the way the redirect is implemented, it can lenghten the loading time by 0,1 to 1 seconds. The loading time of a page is a ranking factor that should not be underestimated. Optimise the loading time of your website and try not to use more than one 301-redirect.

Try to avoid 301- and 302-redirects for internal links altogehter, as they cost time and link power, also called link juice. Google says that there is no high damping factor for 301 redirects, but a little link power will get lost anyhow. Why “waste” it?

From a technical aspect, the Google-Bot will have no problem with following two or even three redirects in a row, if the website performance allows it. If there are four, five or even more redirects, the Google-Bot stops the crawl.

Video explanation by Matt Cutts / Google on this topic

Can too many redirects from a single URL have a negative effect on crawling?

Can too many redirects/multiple hops for a given URL(301 as well as 302) can have negative impact in crawling/indexing/ranking?

Additional information on this topic

Steve Paine