For example, here's a quote from Roy Fielding: "In general, I avoid content negotiation without redirects like the plague because of its effect on caching.". In other words, content negotiation for a versioned content-type is OK... if it redirects to a URL that contains the version.
httpbis, the IETF working group in charge of maintaining and developing the core HTTP spec, has deprecated content negotiation: http://trac.tools.ietf.org/wg/httpbis/ticket/81; it's still part of a separate spec (RFC2295), but it's not a core component of HTTP anymore. Why? 'HTTP content negotiation was one of those "nice in theory" protocol additions that, in practice, didn't work out.'
Certainly you can still build an API that works fine using specialized content types. Versions in the URL are a pretty practical approach that work very well too.