You can do that on ICC (pay) or FICS (free). I believe chess.com is working on adding more of these 'teaching features' as we speak. Skype'ing at the same time is not uncommon. :)
Special analysis software

Here's an option for you ok. Both players would have to start a profile on http://www.freechess.org. (no cost, hence freechess). Player 1 would pull up an examination board (check with site help or admins for commands ((pretty sure it's just 'exa' though)). Player 2 would type 'obs' (to observe) followed by a space and then the name of Player 1. For example, saying you used your same handle on that site, and you were Player 1. You pull up an examination board, and I would check out what you're doing by observing you by typing in 'obs Filipuser'. The one snag is that Player 1 would be the only one able to move the pieces. However, Player 1 and 2 can communicate direct via 'tell ______' and then the message. Hope that is helpful for you.

oic, so on FICS (freechess.org) it's only one-sided. On ICC (chessclub.com) I know myself and another player were able to load a previously saved game, and both of us were able to step through it while trying out the occasional variation.
Hi Everybody!
I have a question which somebody might be able to help me out with...
I'm wondering if there's any (free would be best of course) chess software that allows two persons too hook up with each other over the internet and analyse a game they've just played with the ability to move pieces back and forth just as you would do had your opponent been sitting across the board. (Both persons shall have the ability to move the pieces and take back the moves in order to demonstrate alternate lines).
I know there are many programs out there that let you play in peer-to-peer mode, but is there any program that let's you do what i described above?
If you combine the use of such a software with the use of skype (internet phone) you could have a real treat discussing the games after they are played...
Any thoughts?