Does your oldest checking/savings account ever matter?

Does your oldest checking/savings account ever matter?

So, quick dumb question! I know it's a Bad Idea (TM) under almost all circumstances to close your oldest credit card, even if you don't use it anymore, because the age of your oldest current account factors into your credit score (correct me if I'm wrong, but that's what I've always heard). In my paranoia about having good credit, I'm wondering: is it ever a bad idea to close your oldest checking or savings account? I'd like to ditch my current main checking and savings account because it's started charging me annual fees, and with all the non-fee-charging accounts out there, it's just silly to be paying anything... unless there's some compelling reason to keep it open. Thanks!
.. my bedroom!

.. my bedroom!

Diseased?

Diseased?

Dahlias

Dahlias

Photos From my Garden

Photos From my Garden

First post!

First post!

The last roses

The last roses