Should I assume that attendees have read my papers when I give a talk? On occasion during talks, presenters will say, "as you know from reading my papers" or during a Q&amp;A someone will say "you should know from my papers".

The above clearly seems inappropriate for most settings outside of a group meeting. However, to what extent should I expect my audience to know what I am talking about vs. completely assuming that my audience know nothing?
This really depends on your audience.  


At a department colloquium, I assume very little background, probably an undergrad degree in math, but not even an undergrad class in my research area. Here the audience will often be smart, but ignorant of the relevant background.
At a research seminar with lots of undergrad and/or masters students, I still don't assume much background, maybe an undergrad class in the area, but even then I "remind" the audience of important information they "should" know.
At a research seminar with mainly PhD students and active researchers I assume more, but even here I usually don't assume that they're familiar with the problem or the relevant literature or techniques.
A conference special session (or minisymposium) is similar to a research seminar with mainly PhD students and active researchers.  Here I often expect that much of the audience is familiar with the background and the techniques, but I still usually review them at least briefly.  I've never gotten complaints about giving too much background and context.


I never assume the audience has read any of my papers.
I typically view my talks (at least in part) as advertisements for my papers.  The audience will never want to read my paper if they don't see why it's important (so that's my job during the talk).  For those few that already want to read the paper, I hope they leave my talk with an outline of the paper, which will make it easier to read.  Any time you're talking to an audience with varied background, it's good to briefly describe the key definitions.  If you can do this quickly, perhaps only verbally, you don't bore those who already know, and you give the rest a fighting chance to keep up.