Previous estimates have suggested anywhere between 150 and 3 million.
Bearing in mind the psychological effects and the breeding requirement to keep such a ship going till it reaches its destination and fulfills its mission objectives.
With this is mind I would suggest a crew of 2000. This would allow (with additional sperm and embryo storage) a big enough pool to stop inbreeding and genetic flaws as well as alleviate any negative psychological effects as a result of everyone knowing everyone.
In order to aid a healthy gene pool the crew should be a mix of people from every continent on Earth. This will also act as a true representation of Earth and hopefully act as a tool to unite humanity. There should be a 50/50 male/female ratio and everyone should be of suitable reproduction age.
Departments & skills
Science – Computer, social, physics, biology, chemistry, geologists etc
Medical – A variety of different field specialist doctors.
Engineering – A variety of different field engineers.
Command/Tactical – In-case of communication issues with Earth an independent on-board command.
Civilian – Recreation, social and general non-essential crew.
That’s just my first thoughts, what else? Care to expand?