In the last 15 years I have never had to tell anyone that I've changed my email address. Every personal email address I've given out in that period still lands in my current inbox.
That's not to say that I have't changed email providers. I have several times.  I have just always used email addresses whose destination I can control.
Three of the addresses I have used are actually controlled by someone other than me. My continued use depends on their willingness to continue to provide what I want.
Realizing that I was at their mercy, I decided to get an address that I alone control.

To have an email address that you control, you first have to buy your own domain name. I use  There are others, perhaps cheaper.
The $10.00 per YEAR I pay seems a small price to pay for the control I get.

GoDaddy lets me forward some number (like 100) of email address in my domain to other address. I currently forward the name jim for this domain to my gmail account.
I also have my gmail account set to say that mail that is sent from there is from this domain.

Currently, gmail has the unfortunate feature of adding a line that says "On behalf of".
To eliminate the on behalf of balony, you can open a google apps account.
It's way more complicated but it will give you all the features of gmail and look like it's coming out of your domain.

I will probably be switching to google apps soon.

But if something better comes along, I switch to that. Switching costs nothing because I don't have to change my address.
I just point it to a different provider and get my mail from there.