Online casinos are usually a safe place to have fun. Online casinos operators, at least those who are serious about their operation, recognise that security is extremely important for them to function properly and to provide their services to their clients.
Online gambling activity is done over encrypted connections of military strength which means that no one can intercept and see the information sent back and forth from the client computer to the online casino and vice versa. The information is also stored encrypted so that only selected people can actually view it.