I may be about to start one. It is with someone in another country very far away. We have minimal funding to do this, but we are both starting out on the TT (or local equivalent) and are interested in the science. We have met face to face before at meetings, and this person is a well known and well liked former group mate of one of my current colleagues.
Because of the distance (and lack of funds), we are starting out just sending materials back and forth. The cost of FedEx does add up, though, especially to Far Away. We are hoping to get some nice preliminary data we can then use to get joint funding, and have more actual interactions between the groups. I am not sure how this will work out in the end, since I have never done an international collaboration like this before. For all the talk about how much "smaller" or "flatter" the world is, I really don't see it. I mean Skype is free, but transportation is not. I have done coast to coast in the US, but international shipping rates and airfares are much, much higher (even for the same distance). In the past, I have seen my collaborators from the other coast at least once a year. Not sure how an electronic only collaboration will go.