The Brain Cactus
It's easy to see why these are called "brain cactus." Most of the species in the Stenocactus group include wavy ribs that look vaguely brain-like. Although these plants aren't very common, they are definitely worth snapping up if you see one. Aside from their cool ribs, they also have beautiful flowers and aren't particularly difficult to grow.
Photo © WallyGrom/Flickr
A Great Beginner's Cactus
Also known as the crown cactus, the Rebutia genus includes some great plants for beginners. These attractive plants are fairly typical in their care and quickly form large and very pretty clumps. They readily flower, so the cluster forms a mass of plants and colorful flowers. Even when not in flower, this group includes plants with excellent body and spine coloration.
Photo © WallyGrom/Flickr
Ball Cactus
Now here's a nice little cacti ... the popular ball cactus. This group of cacti includes the Parodia genus, which includes many interesting and easy to grow small ball cactus. Be aware, however, these plants are native to South America and they appreciate a bit more water and a bit less direct sunlight than some of the other desert species. Still, these are easy to grow and an excellent place for beginners.
Powder Puff Cactus
The Mammillaria cactus, also known as the powder puff cactus, is likely the most common cactus grown today, for good reason. Unusually for a cactus, it blooms several times during the summer blooming season, each time bearing a crown of colorful flowers. There are more than 275 species in the genus, ranging from very easy to expert level, so there's something to appeal to anyone.
Photo © Manuel M. Ramos/Flickr
I Thought It Was A Flower Too
I admit it: the first time I saw one of these grafted cacti years ago, I thought the red part was the flower and the green part was the plant. In fact, these very common decorative cacti are grafted specimens. The top is a Gymnocalycium mihanovichii and the bottom is a green columnar cactus that provides the chlorophyll and food to keep the colorful ball alive. These cactus, known as ruby ball cactus, are very common in dish gardens, which makes sense because they are so decorative.
Photo © By Deurs/Flickr
Flowering Sea Urchin Cactus
It's too bad cacti aren't more widely appreciated for their flowers. It's true that dedicated cactus growers know and love their flowers, but I still find enough paper or plastic flowers glued onto cactuses in garden centers to suspect that the general public isn't fully up to speed on how awesome their flowers can be. Well, enter the Echinopsis, or sea urchin cacti. These lovely little columnar cacti have been hybridized to have an incredible array of lovely flowers. 
