I've been a fan of electronic bill payments (either using my CC on the phone or interet, or using bPay to direct debit my bank account) since it became available. But I must admit that electronic bills and statements have never appealed to me. Using free email accounts from netscape or yahoo means that there's always a danger that your emailed statements may disappear - especially using netscape, where your emails get deleted if you don't access your account for 30 days. Also, having to print them out to file them could cost me time and money - whereas getting the paper ones mailed to me costs them money.
So, as most electronic statements (dividends, bank statements etc) would be emailed to you I've always said "no thanks" - up to now. However, I may accept the electronic statement offer I recently got from ING. Firstly, they will store your statements on their site (permanently according to their ad), so I can access it any time via the 'net, and if my electronic statements ever went missing they should retrieve my data for me at no cost (since it's stored on their server).
The second reason is that they currently have a competition for converting to electronic statements - with three $2000 prizes up for grabs.