As everyone else had said HTTPS is a secure end-to-end protocol for web browsing.

You also want to make sure that your e-mail is secure. If you use a browser double check that it's going to a https site -- most do but there are a few services that just broadcast in the clear. If you use an e-mail client like Outlook, secure ports are usually:

POP3 995
SMTP 587 or 465
IMAP 585/993

If you use standard ports like 110/25 anyone in the middle can intercept your messages.

For best security a VPN is about the best solution. I run my own at home & always use it when on the road.
Note that many hotels just subcontract to someone else to provide internet access who might not be the paragon of virtue. A few years back I was at one of the higher-end hotels in Vegas and did some trace routes only to discover my traffic bouncing through way too many suspicious intranet devices, Hotmail should not resolve to a 10.10 address.