What is a good size to accommodate a single-use database for a small application? I'm looking to provision out arbitrarily many sandboxed MySQL databases for anyone to use, similar to how SQLFiddle does, but permanent and with API keys (one database per key), which would allow small developers to set up single-use databases for small applications. What is a sensible upper limit for the drive space I should allow these to take up?
It is generally accepted, by those who study such things in the Big Data realm, that the majority of databases fit within 10 GB. There are many examples of some truly very large databases in the Terabyte to PB range but these are not the norm and I gather not applicable to your use case. Per your description, your use case would appear to easily fall within 10GB or less category. I would further guess you could refine that number for your use case to between 2 to 5GB for "single-use databases for small applications."

If it was my use case, I'd go to the developers and ask to see their local instances of the DB and refine my estimations.