In general? No. There is no general requirement that an IP address have reverse DNS. There is one specific case where a reverse DNS entry can be crucial. Many ISPs block mail from mail servers which don't have valid reverse DNS.

Note the use of the word "valid" in the above. All this means is that the host name which the IP address resolves to has a corresponding A record that points back to the IP address.

For instance, this is perfectly valid:

$ dig +short example.dnsalias.org
70.109.167.222

$ dig +short -x 70.109.167.222
pool-70-109-167-143.man.east.verizon.net.

$ dig +short pool-70-109-167-222.man.east.verizon.net
70.109.167.222

The fact that the IP address doesn't resolve to "example.dnsalias.org" is OK. It's not ideal, but in itself this should not prevent other mail servers from accepting mail sent by a mail server at that IP address (they might block the mail for other reasons, but not due to a lack of reverse DNS).

Technically mail servers using this techinque are using forward confirmed reverse dns which is the full process of resolving the PTR record to a name then the name back to an A record.

Also see - http://tools.ietf.org/html/rfc1912 and http://wiki.junkemailfilter.com/index.php/Fixing_Reverse_DNS for more information.