The general answer to the character recognition problem is negative (currently not possible). However, several important subproblems are solvable. For example, if you know that a particular image came from a printed text, or from handwriting, or a (printed) form, etc, there are some very good solvers. Not perfect (neither is a human, in case of handwriting or a poor fax), but good to very good.

For further googling, see terms ICR, OCR, character recognition.

As a user, I have had very good results with Finereader. Have not tried Tesseract. Parascript was good with online character recognition, but that market is small, and I have not looked at them for a while (disclaimer: I used to work in a previous incarnation of the company).