Can people with student visas "change" them into tourist visas while still in country? In other words, if you will be finishing up your studies, but would like to remain in china for a few more months afterwards, is that possible?

Or do most people need to leave China before their student visa expires, apply for a tourist visa, and then re-enter?

Yes, you can change a student visa into a tourist visa. The school that issued you the visa must apply to have the "X" visa changed, usually requiring a passport photo, a completed application form, and sometimes a short letter (from you) asking for permission to change the visa.

Again, only the school that issued the original visa can apply to have it changed.

Good luck!

I think, but am not sure, that school will change it to an 'L' tourist visa which will be valid for 30 days. I also think that this can be extended once, in country, for a further 30 days.

BUT extensions and new visas could be an issue due to the once in a decade leadership change. There is a precedent for visa refusals at times of high profile events. I was refused a visa during the olympics, and even though I lived in China and had a job, I had to go home.

Thanks. A further question is, is there usually any limit to how many visas one can consecutively get in country. For example, could someone be a student in in China for 3 years without leaving, if they studied 12 months a year (excluding holidays)?

If you are happy studying where you are now, the best thing to do would be to ask them. They will then do everything to support your application, this makes life easier. If they can sign you up for next year now, they will.