One reason I cryptographically scramble identifiers in public URLs is so that the business' rate of growth is not always public.
If the current ids can be deduced simply by creating a new user account or uploading an image, then an outside person can calculate the growth rate (or an upper limit) by doing this on a regular basis and seeing how many ids were used during the elapsed time.
Whether it's stagnating or whether it's exploding exponentially, I want to be able to control the release of this information instead of letting competitors or business analysts be able to deduce it for themselves.
Offline examples of this are invoice and check numbers. If you get billed by or paid by a company on a regular basis, then you can see how many invoices or checks they write in that time period.
Here's a CPAN (Perl) module I maintain that scrambles 32-bit ids using two way encryption based on SkipJack:
http://metacpan.org/pod/Crypt::Skip32
It's a direct translation of the Skip32 algorithm written in C by Greg Rose:
http://www.qualcomm.com.au/PublicationsDocs/skip32.c
Use of this approach maps each 32-bit id into an (effectively random) corresponding 32-bit number which can be reversed back into the original id. You don't have to save anything extra in your database.
I convert the scrambled id into 8 hex digits for displaying in URLs.
Once your ids approach 4.29 billion (32-bits) you'll need to plan for extending the URL structure to support more, but I like having shorter URLs for as long as possible.