A good April Fools day joke is one that is plausible when you hear it, so I wouldn't consider a Radiohead/Nugent collaboration to be a good joke since its not believable at all.
i liked Google's because they were basically making fun of themselves as well,(nose=glass, youtube shutdown=google reader, igoogle, basically every single service they ever shut down)
netflix had a nice day also, they made up a bunch of extremely specific, and amusing recommendations(reality TV that is completely out of touch with reality), took a few that already exist, (I think i got 'Time Travel Shows from the 80's') and put them on your recommendations feed for your enjoyment...
for me it fits your description because i had looked at a few classic Doctor Who episodes...