The most annoying one is usually the block or redirection of port 25 (outgoing email from your machine when you don't use webmail). They often set up a non-encrypted SMTP relay that they want you to use instead. The reason given for this is ostensibly to block SPAMMERs from using their internet service to connect to thousands of open relays out there.

The only reliable way around these blocks is to use a VPN that takes your packets to your desired SMTP server without the hotel network knowing what they are. The other way is to use webmail to send email. It would be good for desktop email clients to become aware of this hassle and provide a way of allowing the user to use his/her favorite client while communicating using webmail on the backend. But I don't think that functionality is widely out there yet.

There are scanning tools out there that will help you find out what is blocked, etc., but I would recommend against using them since conducting the scan might flag you as a suspicious connection and cause trouble.