I also volunteer at a local Mental Health Centre (in Ontario, Canada), and my jobs range from just sitting and talking to clients in the ward, to playing games with them, walking around outside with them (playing catch, etc.), reading, assisting with moving things in their room...well, you get the picture.
It's actually been a great experience, and since the ward I volunteer on has the same clients week after week, you really feel rewarded when you walk in to begin your shift and the clients get super excited and all want to hang out with you. You really feel like you are making their day better.
Most of the clients in this ward are usually afflicted with depression, schizophrenia, personality disorders, etc. (so it's great experience for those wanting to go into clinical psychology). The doctors and nurses who are always in the ward also are super, and they let me take a look and the behind-the-scenes stuff, like measuring out the medication, and have taught me a lot about psychopharmacology. Amazing experience.
Though it's not paid, I think it looks great on a resume/C.V, and it's invaluable experience in the long run. Really makes you think about whether it's the right field for you!