Sounds like there is something wrong with the printer itself. It could be the firmware, so try to reinstall it yourself first. Then reset the printer with the reset button on top of the control panel. Finally, reinstall the driver in your computer as well.
If none of that does the job call Epson tech support. There's not much more you can do at that point, unless you are able to work on the printer yourself.
Thanks for the suggestions Alain.
This problem came on slowly and proceeded to get worse and then suddenly disappeared. Now everything is back to normal and the prints look fine.
A poster on Inkjetart.com suggested removing the ink carts, shaking them and then returning them to the printer. I'll keep both suggestions in mind should this happen again.