LCD clocks powered by a potato used to be sold as novelty items in many stores. I don’t know if they are still available, but that idea is a common science project. But how much current and voltage does a battery like that actually generate? I found a good article by Hans Summers called Homemade batteries that addresses this very question.
The principle behind this type of battery (or wet cell) is very simple: dissimilar metals placed in an appropriate solution will conduct electric current. But the specific materials used are what determines how well it works. To test materials, Hans Summers created batteries using lemons, lemon juice, bleach, salt, and vinegar. Best of all, he logged his results and provided a spreadsheet that you can download including all of his raw data. The article is quite interesting and well worth a look if you have every wondered how far homemade battery technology could be taken.