Libraries and internet cafes are prime targets for keyloggers and are usually rife with malware of all types - including credential stealers - which will happily scrape your passwords and any other form data you enter. It's capable of doing this regardless of whether it is an SSL (https) site you're using or not since the malware is operating with your web browser, not intercepting the traffic after it has been encrypted. These types of threats are known as Man-in-the-Browser credential-stealing botnets.
Whilst I'm not trying to imply that every public computer will
steal all your information, why take the chance when you don't need to?
Incidentally, a good way to avoid keylogging software (or hardware) is to use something like www.lastpass.com
to manage your accounts for you (thus preventing you ever needing to 'type' your password or any other form data, including credit card details, into a website). You can pre-generate a list of OTP (one-time-passwords) which will be entirely useless to any keylogger since (by definition) they only work once.
If you travel a lot and stay in hotels, airports, train stations and coffee shops then I'd strongly recommend always using the above mechanism to protect yourself from personal-information theft. Lastpass is free for desktop use, but I'd also recommend the $12 per year for the mobile client (includes iOS, android & windows mobile).
Hope that helps.