These represent a MUCH bigger risk. You don't know if they are properly configured for security, and so they might already infected with malicious programs that will try to steal data like credit card numbers. If you're in the wrong Internet cafe in the wrong part of the world, the owner might even have deliberately configured all the computers to do this. Even if the proprietor is entirely decent and responsible, remember that the computer you use will be used by someone after you. If you enter personal information while surfing the web in an Internet cafe, this may be cached (saved) by the computer, and could be found by the next user. Our advice to non-experts, therefore, is never to enter any sort of personal information into a public computer, not even your name and address (which can be used to commit identity theft). And don't even think about doing Internet banking or buying something online.
Finally, a thought about using computers belonging to family and friends. If your friend or family member is knowledgeable about computers and responsible, you can assume it will be safe to do Internet banking or whatever from their computer. But if they haven't got a clue about computer security, and have no idea if their computer is safe or not, you might want to think of a diplomatic excuse for not using their computer to shop online... or better still be honest, and tell them to look at this website.