Is there such an option as a catchall subdomain, like www.catchall.mydomain.com?
Something like what you get with some e-mail accounts (catchall@domain.com).

Yes it's called a wildcard and is setup in the zone file for a domain.

It is an asterisk * , but not all DNS providers allow this feature.

Example: *.yourdomain.com placed as an "A" record within your DNS zone file.

If you CAN add it, EVERYONE should since it is quite useful. People will then be able to reach your site if they type:

wwww.yourdomain.com or w.yourdomain.com

Wow!That's interesting!
Yes, I think it would be rather useful! But I have never come across such a feature. It's obviously rarely offered.
Ok, thanks very much Chicken and Smitty!

enom offers it! and there are plenty enom resellers about.

Many DNS providers have this feature as well, but not all.

It is handy, but make sure that you have an "A" record for the actual domain as well, since the wildcard covers ONLY subdomains and NOT the actual domain.

I see many sites that REQUIRE you to use www.thedomain.com and thedomain.com doesn't work. They simply didn't spend a minute and add another DNS record.