Back in the old Windows 95 days, when I was but a wee child in elementary school, there were a handful of fun screen candy applications. One of them was Neko, a cat that would chase your mouse cursor around the screen. I rediscovered it online here, but since that's a Geocities site, and Yahoo! is shutting down Geocities later this year, it's nice to know that archive.org has a copy of the site.
There's also Screen Mates Pumpkin and Sheep. They walk around your screen and use window edges as platforms. Here's a site that seems to have downloads for them, although it says Orange instead of Pumpkin (the original Japanese website for Screen Mates no longer seems available). I think my copies of the programs are from the days when floppies were the way to share programs :)