My first two cats have always been pretty good about the tree. Sometimes they like to use the tree skirt to slide around on the wood floor and occasionally bat at an ornament, but nothing too terrible.
My third cat thought trees were great for climbing and sliding down the branches. Thankfully he's over that now.
This is the first year in a few I've put up a tree. So far no shenanigans whatsoever. I can only hope it continues!