My T gives me homework. Not at every session. I usually do it.
Homework I've gotten: writing down hard situations and what my thoughts/feelings/behaviour were, keeping a journal in which I write down every day positive things that has happen that day, behaviour expiriments (for anxiety), doing more activities outside the house...
My T doesn't push it, it are more like suggestions. If I would say that I don't want to do something, she'll probably ask why I don't want that and what else I could do then. If I don't think something would be useful, then I shouldn't do it just because she suggested it. She also tries to get me to come with suggestions, like how can I handle this. I don't always like homework or doing it, but for me such things are more helpful than if we would only talk. Most of the time she asked about the homework, there have been maybe a few times that she forgot it (or just didn't asked).