The Internet can make life easier! For months now, I haven't put any effort into paying bills. I don't really like bills. Now I don't have to bother with them. My setup includes paperless billing and auto-bill pay (drafts).
Paperless billing means that I do not get bills in the mail. If I want to see details of a bill, I have to log on to my account over the Internet. It's better for the environment because less paper is being used and also less gasoline in transporting that paper. I assume that this is cheaper for companies, so that they do not have to print or mail you a paper bill. It is also probably cheaper for the company because you will be less likely to review your bill for mistakes... which means that they spend less money fixing those mistakes... and also means that if they accidentally overcharge you, you are less likely to catch it.
Auto-bill pay drafts are one type of bill pay option. The easiest option is to authorize the company that bills you (like the electric company) to automatically draft (take) money every month from your checking or credit card account. I set up my utilities to pay the bill in full each month. Many of them allow you to put a limit on how much will be auto-paid per draft. You can set up credit cards to pay the minimum, entire balance, or any amount in between. What's nice about setting up bill pay with drafts is that (1) the bills are paid in full so you don't need to figure out how much to pay and (2) the accounts are marked as paid on the same day. A drawback to this approach is that you end up with more usernames & passwords to remember.
Auto-bill pay from your bank is the other type of bill pay. This option is also easy to set up, but doesn't have the same advantages. In this option, you tell your bank to send a payment to another company or person. If the bank can send the payment electronically, they will do that. If not, then they send a check in the mail. You can set up bank bill pay to happen every month... or you can log on to your bank's website and pay the bills on your own schedule, whenever you want. The drawbacks compared to drafts are: (1) you need to figure out how much to pay for each bill and (2) you have to assume that the bills will be paid around 5 business days after your bank sends the bill pay. However, there are some companies that do not make drafts... for those companies, your only choice is bill pay from the bank.
Of course, a drawback to all of this is that you need to have enough money in your account to cover the bills. Otherwise, you get charged for overdrafts, insufficient funds, etc... which quickly makes this a bad option! You should also be careful to avoid running up your credit card balances.
Justin Pritchard's article on About.com explains How to set up online bill pay.