Minimum? Do you mean what is the maximum number of characters? W3 style recommends 64 characters: http://www.w3.org/Provider/Style/TITLE.html and I think that's a good guideline to go by for google. As far as minimum goes, it can be 0 - you don't have to use any title tag at all. It's poor coding, and it's shooting yourself in the foot in terms of on-page seo factors, but google will index your page even if it doesn't have a title tag, and it will make up a title based on your content.
Well, I have no idea why you would want the minimum number of characters in your title, but there is no minimum. Google will index your page if it has no title at all, or it will index your title if it only has 1 character in it. If the character count is so small, however, they may opt to display a snippet rather than your actual title.