My cabinet is white wood should I prime before painting ?

I would put most of my effort into good prep before painting. Scrub it down with a TSP substitute. When it's dry, sand it, seal it and then paint it.

For the best results... it is all in the preparation... clean to get off any fingerprints and grease... sand, use a good quality primer and a good quality paint... then a clear sealer to help them stand up to washing.

i think it would depend more on the finish of the wood. I mean oil based paint or such.

Even with a white cabinet you will need to clean and prep the wood for paint. A deglosser, cleaner, and just one layer of primer will make a big difference in the final outcome of the whole project.

clean thoroughly first and if you use chalk paint you won't need to prime or sand before painting. there are also quite a few paints that come with prime in them. in those cases you can skip that step too :)

First you need to clean it thoroughly, a good idea would be white vinegar and water mixture since it does not leave a file, then lightly sand all paintable surfaces (this insures a good adhesion to the wood), then I would use Kilz or some form of sealer. Next you paint. It is all in the prep work, if it is not done your cabinets will not look as good as if you had done the prep, trust me, I did not once and hated it for years before I began all over again.