Lots of parents, mostly not pushy or ghastly. The odd cringey question in a talk, although if you're feeling nice you can imagine that the child was feeling too shy to ask.
DD2 and I went on the train to Bristol for their open day - the train was packed with parent-child pairs, and (possibly because it came from London!
) there were a lot of loud, sloaney, "aren't we great" conversations going on. I knew dd had an autobiography in French with her, so I made her get it out and read it, as our contribution to the odd atmosphere
.
Once we actually got to Bristol, it was fine, not even any parent questions in the subject talk :)
Funniest parent encounter was when we went to a post-offer day for dd1's oxbridge college - parents were specifically invited, although at a different time, and for completely different talks to the kids. Dh and I both went (weekend) and were on a tour around, with two other couples. The girl showing us round mentioned the laundry room and the system for paying, and one of the other mums asked, "and is there someone who shows the boys how to use the machines?" 
(Funny follow-up to that story - I don't know who the boy in question was, but the other couple are parents of someone else on dd1's course, who thought until halfway through the term just gone, that the washing machines automatically added washing powder, and so hadn't been adding her own!)