A new finish of paint that is now on the market is matte finish paint. This paint is known for its durability and ability to be washed repeatedly without wearing down or ruining the finish or color. Matte paint is similar to flat finish, but its composition is different, resulting in being able to wash it with soapy water. This is great for a kitchen backsplash because you can easily wipe down the backsplash areas each week to remove food and you won't harm the finish.
Semigloss paint does not have a flat finish. It has a glossy sheen to it when it dries, which protects the surface. This surface is incredibly durable and can be washed as well. If you don't like the flat look of matte paint, semi gloss gives a different look and it also holds up better to the high humidity in a kitchen. Different colors are available so you have a lot of choices for your backsplash look. Semigloss goes on thick so you often won't need to do more than one coat unless you're covering a very dark color.
If you are painting a design or picture on your backsplash, you will want to consider using acrylic paint. Acrylic dries very hard and is very permanent, so once it has set you will be able to wipe over the acrylic and it won't come off or chip. Acrylics also are very affordable and come in many colors, so you'll have no trouble matching your kitchen.
One of the newer paints on the market is black chalkboard paint. This paint can be used in playrooms and bedrooms, but it's also really great for kitchens. Use it on a section of backsplash behind the stove area or countertop. When it dries you can write on it with chalk, then wipe it clean and start over.