I'm having trouble thinking of any situations where you're free to use any alphanumerics, but you absolutely can't use anything else. The closest thing that comes to mind is DNS, and that's a 36-character set, not 62.
Ascii85 (http://en.wikipedia.org/wiki/Base85) uses a similar concept, but using the majority of the printable ASCII characters. It gets a hard-to-beat 20% expansion on binary data (4 bytes in 5 chars) without requiring bigint math.