I can give you the perspective from a candidate having a phone interview. Over the past two months, I've had at least 6 phone interviews and screens. Four of them have led to on-site interviews. I've never had to conduct a phone interview of a candidate, so someone else can shed some light on that side of things.
The best phone interviews have been about the soft side of things. The questions here typically ask about school, work, and various activities. The focus of my best phone interviews that have led to on-site interviews have been all non-technical, focusing on experiences and skills that I have, along with my personality. I think these are the best since this kind of thing typically turns into a conversation between me and the interviewer(s).
By the time the phone interview is over, I like to know if I would like to work for these people. Perhaps not in a technical sense of the technologies that they use, but in terms of the personality of the people interviewing me or by learning more about how the team functions on a day-to-day basis. I like when interviewers take the same approach to me over a phone interview - see if I can fit into the way the team works. When I get off the phone interview (especially if it's the first contact I've had with a team or manager that I would be working under), I have a pretty good idea of how interested I am in the position, but an on-site visit really locks it in.
I dislike when a phone interview begins to get extremely technical. It's not easy for me to show or explain my thought process to you over a phone. I'm probably working on paper or a whiteboard and you can't see exactly what I'm doing. I'm going to try to use words to explain, but I think it's better if you can see my diagrams and thought process. Sure, I might not get the right answer in a quick time frame, but I want to be judged on my thought process. In an interview, I'm put on the spot and should be able to show you how I think and work through a problem, not judged entirely on getting it right or wrong. Ask me about technical things that are relevant to the job that I'm applying for, but don't ask me to produce code or algorithms in great detail over the phone, please.
A few other, random thoughts:
As a perspective candidate, phone interviews are also very awkward. I can't see you, your reactions or expressions, or know if you are about to say something, have competed a thought, or are just taking a short pause. Don't judge based on how the conversation goes, but rather the thoughtfulness and quality of the answers.
If you are going to interview with multiple people on a conference phone, make sure the phone is of a good quality first. I've had interviews where I had to keep asking the interviewers to adjust the phone mic because I couldn't hear one of them. If you have to, perhaps a conference line with everyone on an individual phone would be better. You want to come across professional to me as the phone interview is when I begin to make my first impressions of the team and the organization as a whole.