If machines are the only convenient way to do it then that is what you'll have to do. Sometimes in gyms it's hard to find a situation where all your stations will be open for a circuit.
You certainly do NEED machines for a circuit. You can use bw exercises plus free weights and/or a combination of that and machines. Things like lunges are good because if you are going to do high reps you can probably rely on BW and don't have to worry about it...but also you can probably have access to dumbells if you need it.
It's really simple to design a circuit and you don't have to get all complex. I like to do it antagonistic or "opposites" style but you don't have to adhere to very many rules on that front for this. I like to do lower to upper or back to front...things like that.
And you can mix in anything you like.
Just do some searches and get some ideas that suit you.
Not that you can do something like this but here is a circuit created by Eric Cressey. (I think the guy in lugging tennis balls at him in the background is Eric).
http://youtube.com/watch?v=jA2HIPmVIck&feature=related
(Talo was posting simultaneously).
And this is Craig Ballyntine with a simple bodyweight circuit.