You can have 63 characters in a subdomain, and each character can be one of 26 letters, so 26^63 + 26^62 + 26^61... is the limit. One can also use punycode to increase the limit further.
Edit - no, I'm wrong. That's the technical limit. In reality, bind only allows 16777216 entries per zone.
That's if you're self-hosted. If you're on shared hosting, it's more likely you'll have a limit between 0 and 5.