Either latex or oil-based paint will work well for kitchen cabinets. The main benefit of choosing latex paint is that it is easier to work with since it can be cleaned up with water and dries quickly.
One thing you need to keep in mind if you use latex paint, however, is that it may not be quite as durable as oil-based paint. This is particularly true during the first few weeks after it has been applied since latex paint can take quite awhile to fully cure. After it has cured, however, it can withstand heavy use almost as well as oil-based paint.
According to This Old House, the best type of paint to use is a 100% acrylic latex. Acrylic-based latex paints provide superior adhesion and durability compared to those that are vinyl-based.  Whichever paint you choose, be sure to opt for a semi-gloss finish since flat or eggshell paint finishes tend to be more difficult to clean.
Another option is to use chalk paint. This unique paint has a matte finish that is somewhat similar to the look of chalk. It comes in a variety of different colors and can be applied over any existing finish without having to worry about doing any sanding or prep work. This can make the process of painting cabinets go much faster since preparing the surfaces for painting is often the most time-consuming part of the project.
In most cases, chalk paint will only require one coat to thoroughly cover the surface. This is in contrast to latex or oil-based paint, which both usually require multiple coats. Again, this can be a real time saver.
Another benefit of this paint is that it is non-toxic, odor free, and extremely low in volatile organic compounds (VOCs). 
Once the chalk paint has dried, it can be sealed using a wax to provide a beautiful sheen and extra protection. This video does a great job of demonstrating how effective chalk paint is at painting over pre-finished kitchen cabinets: