I did an informal survey on this issue.
The majority of those surveyed said:
-- they liked the convenience of an e-statement and liked the fact they could get the information more quickly than with a traditional paper statement;
-- they expected the e-statement to have other enhancements and options to make it "better" than the paper statement;
-- they want something to be "in their face" to tell them to go look at their e-statement. Several of the customers had had accounts with an Internet institution that simply stopped sending any hard copy statements at one point. It never emailed the customers to let them know their statement was online. Many of them were not using this institution for their primary accounts, but had opened the account somewhat for the novelty of it. Without the emails or the hard copies of statements, the institution was quickly "out of sight, out of mind" and lost out on the opportunity to solidify customer relationships and cross-sell.