Hi Elaine! The best way to paint kitchen cabinets without sanding them is with a chalk based paint. I love Annie Sloan, I've also used Dixie Belle and Jolie. You can check out my post on how to paint kitchen cabinets here. :)
There are many products out there nowadays that allow you to paint cabinets without sanding them first.
Dixie Belle chalk paint is great! they sell a cleaning product that removes all of the grime on wood - even if you have washed it before!
I haven't used this product, but it has pretty good reviews on amazon and is intended for kitchen cabinet makeovers with no sanding.
I highly recommend using this bonding primer (here is the affiliate shopping link for it). No sanding, just prime and paint. It works great!!!
Chalk paint is great no priming or sanding required. I love Decoart's chalk paint. You can get some from Amazon here.
You can buy paint that wool go over any kind of wood. Ask the professional at the paint store.