Paperless is great for all bills
BUT
make sure you keep up and print yourself out a hard copy maybe every quarter or something for your reference, and taxes if you need it.
Some places don't let you access more than a year back or so, so if you need to look at it or if you file an October extension for your taxes and you go back to look at your . . energy bill from 18 months ago you might not be able to find it.