A couple of ways to look at it.
In most of the US, you don't need a written agreement to take photos of people, and you don't need a model release (or even their knowledge and consent) to use the images in a non-commercial manner - even selling prints as art is not always considered commercial. However, to use another person's likeness in a commercial manner (advertising, product packaging, etc) then you need a model release.
Since I don't know what country you're in, I don't know whether this applies to you.
However, even if no money is changing hands, and even if you won't be using the images commercially, it's a fantastic idea to have a written agreement drafted up and agreed to by all parties, before the shoot. That way, everyone knows exactly what to expect, and when to expect it. Perhaps the model will expect to receive 200 photos on a disc at the end of a 1-hour shoot, but you expect to give her 6 edited images on a disc, a week after a shoot. Unless you discuss it beforehand (and write it down) then someone's expectations will not be met.
The vast majority of the time, you can get away without any written agreement. But when the day comes that you have a disappointed or angry model on your hands, you may wish you had taken the time to get that piece of paper.
Also, in the US (and most of the world), you retain the copyright to the image, but you allow the model or client to use the image, by way of a licensing agreement. Just because the other person appears in the image, DOES NOT give them any sort of copyright or legal rights to the image, unless you grant them a license to use it.