That may just be an American thing though, countries with first world banking systems may have that sorted :)
I get a bill. At the bottom of the bill is a red pay-in slip with a magic number on it. I log in to my bank, enter the number, tell it how much I want to transfer, done.
There's a not-used-enough automatic system where one of my creditors can send their bills directly to my bank. Now, I log into my bank, get told there's a pending e-bill, at which point I select it, press 'pay', done.
No fees anywhere.
I'm from the UK, which is just starting to do this, but it's nothing like as polished; small traders and tradesmen still prefer cheques, and regular payments are typically done via direct debit, where you authorise them to debit money directly out of your bank account (with a whole pile of banking guarantees). Switzerland seems to do this much less frequently; most people just pay the invoices monthly.
Plus transfers are free... and appear same day in the other account.
The US is a different kettle of fish.
---EDIT---
Wire-transfers between national banks are free if you wait a day; there's a small fixed fee if you want them immediately. Transfers between different clients in the same bank are free and immediate. And it's becoming very common to be able to pay a quite assorted list of services through your e-bank account (from utilities to departmental store accounts) without fees.