How many sub-domains can there be at most?

The limit would be dependant upon the DNS server, not the webserver. BIND allows for 16777216. Microsoft DNS is said to be stable to 20K objects per zone. Regardless, Peter is correct. It is too large to matter unless you are doing something non-standard.

To clarify, the longest domain name possible is 255 characters with no label (peice between dots) to be longer than 63 characters per DNS spec.

The only limit is the length of the URL - the subdomains are interpreted by the webserver. (And that means there's no relevant limit, by the way - the number is just too huge.)

EDIT: the maximum length of the URL is 253 octets, or 253 characters if using ascii. That's plenty :)