I've been paying my bills via on-line for 2-3 years. I like it; it takes me about 15 minutes, and I know that all the bills are paid. I haven't lost the envelopes on the way to the post office; the bills aren't lost in the mail, etc.
I make sure to get a 'receipt'. I keep an eye out on my account so I know when they are cleared through the bank.
Nothing against the US Post Office. I still send packages out through them as they have the cheaper rates.