I think it depends on if the "Compare at" price is an honest price. We use "compare at," "list price" and "our price" on our website.
In our shop, "Compare at" and "list price" are the same thing, and are set at what we see the same or similar goods selling for in local quilt shops. This might not be the cheapest price you can buy it for, but is the price many shoppers see when they're out and about shopping, so we think it's an honest price to quote.
I'm not sure that it really makes a difference to a lot of shoppers, since many if not most internet shoppers are doing a lot of comparison shopping, and they know where and at what price they can get what they are looking for. But I do think it's a valuable tool in that it gives people an idea what they would pay if they were shopping at many stores. Like most marketing tools, it has a limited purpose, but a purpose indeed.