We have a number of Billy bookcases, and they are not secured to the wall. On the other hand, they are all shimmed slightly in the front (one layer of corrugated cardboard) to ensure they get support from the wall, so we have a bit of security there.

Fortunately, NOche, the newish (October 2007) cat who happens to be a bouncy menace, and an up-cat as well, prefers the top of the fridge (as well as the childrens' dressers, shelves, and the bathroom sink). Knock on wood (or pressboard, as it were :-) she won't, even now that I've mentioned it.