This is always being debated, and as new research keeps coming out the question seems to get more, not less complicated. It is one aspect of the old nature versus nurture debate, which is still causing arguments.

There are some conditions and disorders which do often have a genetic component - such as some types of schizophrenia or autistic conditions. So at one end of the scale, genetics clearly plays a major role. It's also increasingly thought that some forms of depression - which of course has a big impact on personaiity - are genetic too, and - though this is more debated - certain abilities such as creativity. This is much harder to measure, though.

Whether certain people are just likely from birth to be happier, or more confident than others, or more aggressive or whatever, is still not certain. The problem is that environmental factors, which also influence personality, begin in the womb and are in force from the moment of birth, so we are still a long way from being able to separate them.