This is one of those complicated questions, because the answer is both yes and no. Many people believe that stucco should never be painted, because, 50 years ago when oil paint was the only option, this was true. Never use oil paint on stucco. Stucco, like masonry in general, needs to breathe, to accept and release moisture as the weather conditions change. Oil paint will act as a vapor barrier, and there's a good chance the stucco underneath will crumble, leading to some serious peeling and flaking.

 However, there are several modern, latex paints that have been formulated with stucco in mind, and they work beautifully. Painting stucco can cover the patches that have been made, erase the seams between an addition and the original structure, and brighten the sometimes depressing greyness of untinted stucco. This brings me to another thing: although not always true, sometimes the original stucco can be historically important (I'm thinking here of the interesting sand textures and tinting on a Percell & Emsley house here in Minneapolis) and painting over this is a crime. An architectural crime! Don't be a perpetrator.

Painting stucco is, in some ways, easier than painting wooden siding. The first step is to get the stucco clean.  This is best done with a pressure washer.  The next step is to remove any loose paint, if the stucco has been previously painted.  The pressure washing should remove most of the loose paint, but it may be necessary to scrape or wire brush some spots.  Now is the time to fix any spots where the stucco has fallen out.   Once any patching has been done and is dry, it’s time to prime.  Stucco and wood are different surfaces, so a traditional wood primer may not be appropriate for priming stucco.  Check the can’s label or ask your paint store sales rep to make sure.  Sherwin-Williams sells a product called Loxon XP which acts as both a quality stucco primer and top-coat.  After priming, caulk any cracks and apply the finish coat.  If the stucco has been properly primed, any high quality latex finish paint can be used for the final coat.