The threat of phishing (attempting to gain access to confidential information by tricking the victim into thinking the request is legitimate) is as real as ever. Some of these scams are more obvious than others.
This is the closest to the concept of changing your email to reduce phishing. Most internet service providers typically offer a set number of free email addresses to use as part of their service package when you sign up Email1and1. These are probably for each family member to have an email address. You can also get free email from providers like google and hotmail.
One strategy that can be adopted is what I call distributed email. Here you split up the people and organisations who can contact you by email into groups or categories. Then you set up a different email for yourself for each group you have identified. So if you do online banking you may want an email just for your bank account. Then another for your memberships, clubs etc, another for your online shopping accounts and another for your friends and/or family.
The concept to this is that the smaller the group you assign to each email the less that email gets used and the less exposure it has over the internet to be skimmed by robots for phishing purposes. A little bit of planning here can do wonders for how well this strategy will serve you. As the email addresses from your internet service provider are probably paid for you are more likely to receive support from your provider if something goes wrong. It makes sense therefore to use these emails for important contacts like your bank. It also means that your service provider will be actively monitoring traffic on their server for suspicious activity and be filtering traffic out if it starts causing problems.
You could also think about using a service provider and public email providers that offer automatic forwarding of emails. Doing this can make this approach work even better for you. This is because once you have set up all your email addresses you can then have just one email address that you actually use (preferably one of the ones your service provider lets you set up). Now go into each of the other email accounts and do two things. a) Set each of them up to block all traffic into them except for the users that you know will be sending traffic to that email. So the email for the bank will block all traffic except for emails from the bank.