'The Modern Prometheus' is the subtitle to the story and is very revealing. It gives a very strong hint as to how we are really meant to take the character of Frankenstein.
In classical mythology, Prometheus was one of the Titans, an ancient, immortal, immensely powerful race. He was said to have created the race of men. Zeus, king of the ruling Olympian gods, did not think much of this new race, but Prometheus did all he could for them. His most famous exploit was the stealing of fire from heaven in order to benefit mankind, but he paid the price for his presumption. This act enraged Zeus, who ordered Prometheus to be chained to a rock where an eagle pecked out his liver every night. According to some sources, this punishment lasted all of thirty thousand years, until he was finally freed by the great (and, incidentally, half-human) hero Heracles.
The story of Prometheus, then, has clear parallels with that of Frankenstein. He created man just as Frankenstein also creates a new, sentient creature, and he further defied the ruling gods in order to bring the forbidden art of fire to his creation. Therefore he was responsible not just for the creation but also for the advancement of mankind. He sought to bring knowledge and advancement to humans, just as Frankenstein seeks to push back the boundaries of human knowledge and achievement. However, both Prometheus and Frankenstein are seen to go too far, challenging the gods, raising the bar too high for mere human mortals. Both incur fearful, long-lasting retribution - although Frankenstein is not finally released from his torment, as Prometheus is (although, of course, one might view his death as a kind of release).
Frankenstein's comparison to Prometheus, then, is highly significant. It suggests a certain noble, heroic strain in the character, as well as his being fated to a lifetime of suffering for his actions. The story of Prometheus is one of the most well-known of classical myths and had particular currency in the British Romantic period (when Frankenstein was written) which extolled the image of Prometheus as a tragic, isolated hero, a great striver after human achievement, as well as an inspired creator, challenger of the gods, and the lonely sufferer. All these traits are also present in Frankenstein. It is not surprising, then, that Shelley used this as the subtitle to the novel.