I don’t know of any plugins that do this, and I’m not sure you’ll find one. The closest I can find is the “Mandatory Field” plugin. The specific tasks that you might want are so varied, that I wonder whether a non-bloated plugin that let you customize the validation is out there.
With that said, you’ll want to look into the save_post hook. There are quite a few questions about that hook on this very site (such as this one). If you’re looking for a code-snippet to modify, I’d start by looking through those questions.
Also, even if you do manage to write a good validation plugin with the save_post hook (btw, I’d use the term “validation” in your future questions and queries as that’s really what you’re trying to accomplish), I’d consider augmenting it with some client-side jQuery validation. I’d imagine it would be very annoying to have the “Publish” or “Update” button not take the expected action since this is a relatively rare feature to add to a WordPress site. By creating some live validation (backed up by the server-side stuff) would be a much better user experience.