About 10 - 20 years ago, it was called faux painting and was hot in home decor. Now, sponge painting and those faux textures are truly dated. However, decorative painting with glazes, paint effects, and antiquing is incredibly popular and on trend right now. See some beautiful examples like the photo here.
Note, your local paint store sells many glazes and decorative paints. Just ask and most will be glad to give you helpful hints to do it yourself.
[Editor Note: Photo courtesy of www.styleblueprint.com]