Online banking rocks! Like the OP said though don't believe emails. In today's world though with $300 laptops is easy enough to have one computer used solely for online banking and never for email.
But we are all different and that is part of what makes life so much fun. aloha

Never, ever respond directly to email in your Junk email folder. Set up rules that move email from KNOWN email addresses to other folders and work there. Don't trust links purported to be from your financial institution. Right-click or hover over the link to see the real URL. You will frequently find the URL is from some one in Russia or somewhere else you don't want to go.

Think about it. With increased convenience comes increased responsibility. By now, everyone should have all of your email addresses, hat tip to our friends at the NSA. I have several; my company email, my personal one, the one I use to for porn websites ( NOT! , well not me but others may ). If you receive an unsolicited email from a financial institution, eBay, PayPal, et al., your first response should be to never log in using the email message, but go to the website as you normally would. Your email application may be able to show you exactly where the email originated from.

It's just like anything else online. As long as you're smart about it, the chances of getting duped drop immensely. Carrying your wallet outside can also lead to your information being stolen. The only difference is, you don't readily see the paths attackers take when you're online.