Optical Character Recognition (OCR) of ancient Greek polytonic scripts is a challenging task due to the large number of character classes, resulting from variations of diacritical marks on the vowel letters. Classical OCR systems require a character segmentation phase, which in the case of Greek polytonic scripts is the main source of errors that finally affects the overall OCR performance. This paper suggests a character segmentation free HMM-based recognition system and compares its performance with other commercial, open source, and state-of-the art OCR systems. The evaluation has been carried out on a challenging novel dataset of Greek polytonic degraded texts and has shown that HMM-based OCR yields character and word level error rates of 8.61% and 25.30% respectively, which outperforms most of the available OCR systems and it is comparable with the performance of the state-of-the-art system based on LSTM Networks proposed recently.