I enjoy my prayer group at work a lot, but I've been in other prayer groups that didn't work. I think the problem with the ones that don't work is that nobody is in charge. Here's how things go wrong:
People get together and eventually someone (hopefully) suggests that people share prayer requests, and people do, but they also chat about various other topics, then other people chime in and it becomes a general conversation. Then, about three minutes before the available time ends, somebody says, "Ohh, we're running out of time. John, would you pray for us?" So John prays a brief prayer and that's that. So, the few gregarious people are prayed for, the others miss out entirely, and the prayer time is perfunctory. Even worse, I've frequently seen instances when the time runs out and the group never gets to prayer.
I lead a group at work, and I think the solution is one person committed to watching the time, getting the requests out and making sure there is enough time to pray. I try to keep things on track by summarizing a person's requests. If I sense the conversation beginning to wander too far, I'll say, "So the things we can pray about for you are A, B and C. Are there any other things?" This tends to bring things back on topic. Also, I don't ask who has a request, we just go around the circle. That way even the shy people get a chance to share.
If I were to join a new prayer group, I think my first question would be, "Who's the timekeeper?" And if there wasn't one, I'd request that there be one. And if I couldn't get that, I think I'd decline to participate.