For most of us, a compromise on an email account could mean a compromise on a dozen connected accounts. Its always a good practice to have separate public and private email addresses. A public email address that your would use to subscribe to online services such Facebook, twitter, LinkedIn, Flickr, Quora and several other sites and a private one that can be associated with Bank Accounts, Hosting Company, PayPal, Amazon, Online file hosting service and any other place where account security is even more critical.
Having separate email addresses combined with a strong password maybe the best security measure but if you are a Gmail user there are other basic, yet important steps that you can take to make your Gmail even more safe and secure.
Here are two videos from Google. One providing the very basic Gmail security tips and the other about the recently introduced — 2 Step Verification method.