I hate having to figure out THE PRICE for products and services. I used to work in the computer goods industry and we had lots of products that lost their value very quickly. You wanted to maximize your margin but minimize your shelf time. Get the equation right and you made good money. Get it wrong and 7% average value depreciation per month - ouch! Yes that product was pretty much worthless by the end of one year. How did we handle this scenario, we cheated. We'd volume discount and create lots of ways to lower the price "without lowering the price" - instant rebates, spifs, rebates, multi-item discounts, etc. It was a mess to create, mess to track and ultimately everyone felt cheated.
Well many different kinds of businesses have asked that exact same question and said leave it up to the customer. Let them name their own price. For many that may sound like sacrilige - everyone will want it free or as close as they can possibly make it to free and indeed some will work the system as tightly as they can. So why do it? There can be lots of reasons.
People will pay for what they value and the more they value it the more they will pay. If you are focused on the value of your products and services and you believe you are successful then you may actually make more money by allowing your customers to determine how much they want to pay.
You may have a kind of business that is highly scalable - think web services and software. If it basically costs you nothing to distribute your services or software (online download) then any dollar you bring in is one dollar more than you had.
You may be a services company that is seasonal or has underutilized overhead. This applies to dog groomers, accountants, skilled labor and consultants. If you have time and it's not billable you have opportunity costs eating away at you.
Maybe you have products and services with no real shelf life- a bakery, a ski resort or an airplane. There is no bottle to put the Genie into so why not sell out all the time.
You can try the idea of name your price without jumping in with both feet. You could do a temporary "special" and you can offer the program to a limited pool. If it gets the results you want then put it in full time or use it as a promotional tool when you like.
Of course you may have underlying costs, production, overhead, etc. You can always put a floor on your named pricing but don't bait and switch. If you don't have at least 50% swing in pricing then I don't know you're doing anything more than a discount special. You can also help position a floor in the minds of your customers through your marketing - "this combination of services normally goes for up to $495 but for today you get to name your own price".
If price is bothering you and you want to try something new then let your customers name their price.