If it helps anyone, when I was doing my teaching experience a few years back, I got presents from some of the children (though mum/dad probably brought them). These presents were typically a bar of chocolate (a big 500g bar, or 1kg bar). I think the children got the impression I had a sweet tooth! As a student teacher, I didn't expect to get anything, so it was great when the children gave me something - it's not what the gift is, its the fact that the child (or parent) felt a present would be nice.
As a freelance nanny, I give the children I care for on a regular basis a present at christmas time. Due to my relationship with the families, I often get presents back as well. I put this down to being 'part of the family'.
wendym - I think you are right to give to nursery/teacher/sunday school teacher... and not to give to gym/swimming club teacher.
My view is that if your child spends a long time with someone, then that person should have a present (for example, Nursery Keyworker, Class Teacher, Childminder, Nanny etc.) but those people who do not see the child on a regular basis should not really get a present.
For those of you with children old enough... ask them who they want to give a present to. Children will say who they like and even come up with present ideas - a mug with their picture on for example. It's not what the present is that counts, but who it is giving the present - so if you can, let your child choose the present and whom to give it to.
Just my thoughts.