Favigen is a free online tool, which allows a user to create a favicon for their website.
To create your own favicon, browse to the image on your computer that you want to create a favicon of, select the dimensions, and click the big Submit button.
After generating the favicon, it will be displayed on the site from where you can download it.
Favigen can generate favicon of 16×16, 32×32 and 64×64 pixels. It supports image formats like jpg and png, and it does not seem to have a file size restriction either. Simple instructions are provided on Favigen on how you can add the favicon to your website.