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I'd rather go to each individual site to pay the bill, than have one site with ALL my sensitive financial information in one database.
A lot of credit card companies offer account aggregation services through their sites, so if you have credit cards, you might want to check out their sites... they don't let you directly pay through them, but you can view your account info in one place, and then it's usually a one-click deal to visit each bill's site and log in to pay it.
I was an early adopter (sometime in 2000) and LOVE it. I highly recommend the service.
They've consistently gone above and beyond to help me when I've needed help and take care of things for me.
I was going to switch to Bank of America's bill pay service because it's free, but I tried it for a few months and switched back - features/functionality were not as good and I didn't feel like they were very helpful.
<edit>added BofA comment</edit>
Anyway, I'm able to pay all of my bills through their interface. If I'm not mistaken, you should be able add payees to your bill pay interface. Half of my bills are fixed expenses so I have recurring payments set up based on the billing periods.