Omicron Persei is a binary star. I did not find information on how many planets it has and if we can actually determine it currently. However, I do know that most stars have planets orbiting around them and so I assume there are such planets.
For those who are interested, Futurama featured the planet Omicron Persei 8 - the 8th planet in that system. I was curious as to if there is an 8th planet.
Currently http://exoplanet.eu/ (which lists more exoplanets than the official NASA archive) lists no known planets of Omicron Persei. So currently we know of none, it is outside of the Kepler field so has no Kepler candidates either.
Though just because none are known that does not mean it has none, it may be that their mass and or orbital plane is such that it is very difficult to identify planets or no one has looked with a suitable instrument.