I have been experimenting with GMing by means of the InterNet since my gaming friends from university scattered to the ends of the Earth, which happened in the early nineties.
The first thing we tried was RP by e-mail. But that was too slow: it lacked interactivity and personal contact and turned out like a giant, very complicated collaborative writing process. I have archivesâ€¦.
Then when we got InterNet text chat we tried using that. The problem there was that I am not a very fast typist, while everyone else found that in text chat you can keep on composing continuously, without having to hold you tongue while others are speaking. As GM I got snowed under, everyone turned to side chatter, and the game content drowned in badinage.
Next up was VoIP conference calls. I can't remember whether we started with Skype or with iChatAV. That worked well, with two slight problems.
(1) First was the lack of a table, scratch paper, hex mats etc., which meant that we couldn't use any rules that depended on detailed positional information, and that it sometimes because troublesome even to give general positional info. I took to preparing maps and diagrams as graphics files and sending then to players as needed. But it helped a lot that our preferred style of play was highly narrative with little interest in tactical combat rules.
(2) Second, and more trying from my point of view, was the lack of posture, gesture, and facial expression as communication channels. I found it surprisingly hard to understand some speakers when I couldn't see their mouths move. (I had my hearing checked: the doctor told me to get friends who don't mumble.) Also, we found that there was some difficulty in cueing people as to when it was their turn to speak. A couple of times I played with two or three former military men, who used radio protocols. If you find that too stilted, I'm sure that it would just be a matter of cultivating such habits as diligently addressing people by name, addressing remarks and questions to individuals, and a few tricks like that.
Nowadays I do almost all my RP by means of InterNet video conferences. I'm sure Skype would work fine on other machines, but it doesn't do multi-party video chat on Macs. iChatAV is excellent for the purpose, but it only runs on Macs. So mostly we use Google+ Hangouts as our videoconferencing solution. Results are very good while each player has his own camera and stays close to his mic. Background noise becomes a serious problem when several people try to playing one room four metres from the webcam and using a room pickup.
The chief lack is a way of quickly conveying a sketch-map or diagram. We use a virtual whiteboard (such as Sciblink or Twiddla). Results are okay, but it's a bit small, sketching is slow, and accurate erasure is difficult. We're still trying to nut out a solution in which a hex-mat on the GM's desk gets its own webcam and channel. We did try using a suite of virtual classroom software (called "Colloquy", I think), but we had technical issues with it, and some players weren't happy about the involved installation.