There are two big advantages to windowless aircraft:
- Design complexity/structure
Cost is a fairly obvious one; the plexiglass used for aeroplane windows is not expensive, but designing around it increases costs all the way from conception to manufacture of an airliner. Plus the airline needs to think about blinds/curtains, seat placement, and the extra processes involved in cleaning all the windows on the aircraft regularly - inside and out.
To the second point: design. Not only do windows complicate the design of an aircraft (thus increasing the cost) but they're also structural weak points. An aerospace engineer would like nothing more than a simple tubular fuselage without these vulnerable stress points (aircraft windows are round rather than rectangular to reduce these).
Here's an interesting example of a windowless concept aircraft: the Reaction Engines A2. This hypersonic aircraft flies so high and so fast that the stresses and heat on the fuselage are simply too much for big windows to handle. Any windows would have to be tiny (like on Concorde) - so they're simply left out.
So to sum up: windowless aircraft certainly an option for future superfast and high-altitude air travel, but for today's commercial airliners the only point would be a slight saving in cost. Whether the idea of a windowless airliner would affect passenger number is unknown, but I imagine a lot of people would be uncomfortable with the idea.