You can play blinfold chess on FICS (http://www.freechess.org/) if I remember correctly.
Live Blindfold Chess

vowles, it's already in our plans to add it to live. :-) glad you'll enjoy it.
Shweet! Thanks David! Do you have a rough idea when it will be up and running?
I look forward to it!

Funny that EpicJohnston and I both replied to this on the same day after 17 months of inactivity.
Anyways, I went onto FICS and their blindfold feature is practically useless. You have to apply to play blindfolded and they can deny the application for several completely unsabstantiated reasons. For example, you can be denied for not having played at least 15 hundred games of chess on their server.
The ability to play blindfold chess helps any player improve, and is something that would take almost no effort to implement, assuming a blindfolded player could play against someone playing with a board. Is it safe to assume the idea has just been trashed?
In the same way that people can select the piece design for analysis and creating puzzles, could they just edit it to have the design image of each piece to be blank?
Otherwise, could chess.com acquire the software used in the blindfold tournaments where they play with a blank board?
I'd really love to see this happen, I think it would attract a lot more people (even though chess.com is quite large already).

I would be interested to know the state of development of this project (if there has been any!), if the information is available.

I read here that within a week there will be live blindfold on chess.com!

Hey vowles. The members playing vs GM Timur will see the board, it is only blindfold for him. "On game day, Timur will open up for challenges at 2:00pm Pacific, 5:00pm Eastern - and members will have an opportunity to compete against him on a first-come / first-served basis. (Unlike Timur, these lucky members will, of course, be able to see all the pieces during their game!)"
Recently, I have been looking into playing blindfold chess online, to find that you cannot play live blindfold chess on the internet! (However, schemingmind.com allows corrospondance blindfold chess.)
I think that this would be a very attractive feature for chess.com to have and will draw more people to this website. Also, I doubt that it would to too difficult to set up and get running, as the rules are all the same, etc.
As it is live, I doubt that cheating would be too much of an issue, although I'm sure some would try. However, I think it would still be benefitial for improving chess players to have access to this feature.