When I strum a chord, do some picking, etc, I've got this strange buzzing sound coming out of it.

Does anybody know what can cause it?
Buzzing is caused by bad frets, truss rod, or action. If it is an old guitar that has been played alot then the frets most likely need to be redone. The truss rod should get adjusted every few months and such depending on were you live and what the climate is like there. As far as the action goes, if you have the action to low then that will cause buzzing. All three of these problems concern, a guitar tech at you local shop can deal with them or if you are a little more adventours there are crap loads of books.
Well, it's an old (a minimum of 30 years) spanish/classic acoustic guitar, so no truss rod here, also the buzzing is not coming from the frets, it's coming from inside the body itself.

When I apply some pressure on the body (just touch it is enough) the buzzing stops.
It's possible that one of the inside trusses is loose. If you have a mirror try and get that inside and see if somewere the wood glue is coming loose.
hmm i guess i'll have to fetch my sis' make-up mirror...

I guess it is the first truss, because it dropped out before... We glued it in place again but I guess it got loose again.
It would be a shame if the guitar is ruined, because I love the sound of it