You've probably seen cacti (and sometimes other succulents) with small dried flowers stuck to them in rings round the top. You may also have noticed small cacti with small real flowers (I mean the flowers of the cactus) in rings round the top. I think the dried flowers are meant to imitate the real flowers that belong to the most popular genus of cacti Mammillaria. There are probably several species in the cactus section of your local garden centre. Oddly, for such a popular and common genus, Mammillaria has no generally recognised common name and the Latin name hasn't made its way into common usage.
This article is about plants that don't have common names so it's going to contain a lot of Latin names. You can use a search engine to look these up.
Mammillarias are desert type cacti in the sub-family Cactoideae, which means that they have fleshy (almost always) spiny stems with no leaves (although some have very large tubercles). The stems are normally green but some species have a lot of red pigments making them look brown. They're fairly small, usually less than 30cm high although some can form clumps 1m or so across. The flowers are usually only about 1cm across and produced in rings around the growing tips. They all have spirally arranged tubercles (bumps) with no sign of ribs (ridges). Unlike most cacti, the areoles (hairy patches that produce the spins and flowers all cacti and only cacti have them) are divided into spine producing parts, which are at the tips of the tubercles and flower/branch producing parts that are in the tubercle axils. If you look carefully, you will often see a small hairy patch at the base and above each tubercle. If your plant has flowers or branches, you will see that these also come from the axils (some species branch dichotomously and one oddball has flowers from both the tubercle axils and tubercle tips). They DO NOT have nectar secreting glands or groves on the upper side of the tubercles (if your plant has one or both of these things, it's probably a Coryphantha or Escorbaria). Almost all Mammillarias are native to North America and most are Mexican.
Each areole will normally have one or several central spines that arise from near the middle and point out from the plant. There are normally a greater number of radial spines that arise from the edge and point sideways, around the plant. This is true both for cacti generally and Mammillaria generally. Some Mammillarias have only central spines. Many have only radial spines. There are no spineless species. In many species one central spine is hooked so it's sharp end points towards the plant and tends to catch on things (a feature found in only a few cactus genera).
Most Mammillarias have flowers about 1cm wide and long, just long enough to get the open end past the tubercles and radial spines.
Sorry if this is sounding a bit technical but it's hard to put things in simple terms because Mammillarias are very varied in general appearance, this is part of why they're so popular with cactus collectors. Also, as they're small, you can grow them from seed to flowering size in a couple of years and keep many mature plants in a small space. They can also be propagated from cuttings (sometimes single tubercles will grow), which is useful for the clustering species. Taking cuttings makes a mess of the single stemmed or dichotomously branching species but it can save part(s) of a damaged or sick plant. Mammillarias can also be grafted onto other cacti (they're rarely used a grafting stock), to make them grow faster or more easily.
Generally Mammillarias grow well with normal desert cactus treatment: bright light, a well drained compost, watering (preferably with rain water) about once a week from spring to autumn and none in the winter and being kept cool but protected from frost in the winter. However there's a fair degree of variation, some species being very easy to grow and others about impossible.
Many attempts have been made to bring order to this rather confused genus either as a system of sub-generic groupings or splitting into multiple genera. Some have attempted to split the genus roughly in half by dividing species according to milky or watery sap or straight or hooked spines (both of these characteristics are variable in some species). Often more unusual groups or single species have been separated into sub-genera or genera: Solisia for M. pectinifera, Mamillopsis for M. senilis, Cochemiea for M. poselgeri, M. halei etc, Dolichothele for M. longimamma, M. surculosa and sometimes M. camptotricha and then things got complicated.
As this is an article and not a book, I'll just look at some of the more noteworthy species.
There are a number of smaller, clumping species with small flowers, which are mostly easy to grow.
M. vetula ssp. gracilis (also called M. gracilis) is probably the easiest species (or subspecies) to grow. This is an unusual plant with short cylindrical stems and relatively short tubercles with weak, spreading spines. The whitish flowers are rarely produced but it has an unusual habit of producing branches in rings around the top. These are easily detached and take root easily.
M. prolifera lives up to its name with fast growth and very easy culture. It's also one of the more resistant to cold temperatures. Forms clumps of small heads covered in white hair and straight brown spines. The flowers are an unusual apricot colour and are followed by red berries.
M. camptotricha has very long pointed tubercles and long, curved yellow spines. It looks like some sort of deranged bird's nest but it's very easy to grow. The flowers are white.
M. bocasana is another hairy one, this time with bigger heads and hooked spines. The flowers are silvery white or pink and followed by very long curved, red fruit.
M. zeilmanniana looks like a less hairy M. bocasana but has dark purple flowers.
M. plumosa, as the name implies, has white, feathery spines that completely cover the plant. It normally has green flowers in the winter but occasionally has purple flowers in the summer.
M. carmenae and M. laui are rather similar with fluffy white of yellow spines and white or pink flowers.
M. elongata, as the name suggests has relatively long stems. It also has spines in a wide range of colours (mostly shades of yellow, red or brown) and white flowers.
Large single stemmed or dichotomously branching, small flowers.
Beginners are probably best advised to start with some of the previous group. Next people normally move onto these. Dichotomous branching is where the growing tip divides into two to produce a forked stem. It's unusual in cacti.
M. rhodantha is rather varied with mostly yellowish or brownish spines and red flowers.
M. pringlii has yellow spines and small purple flowers. In my experience, it grows surprisingly quickly from seed.
M. haageana is smaller than the previous two with dense white hair, short spines and purple flowers.
Mostly disc shaped plants with pyramid shaped tubercles.
These don't seem to cluster much and are of normal ease of cultivation.
M hyederi has white flowers with a greenish stripe. Its variety bullingtoniana is probably the hardiest Mammillaria.
Large tubercles and large yellow flowers (sub-genus Dolichothele).
Unlike most the large flowered species these are fairly easy to grow. Also yellow is an unusual colour for Mammillaria flowers. They like large pots for their fleshy roots and lots of water and fertilizer (by cactus standards) in the summer.
M. longimamma is quiet a large plant with very large flowers.
M. baumii has white hairy spines.
M. surculosa is very small and forms clumps.
Small plants with average sized flowers (mostly with few petals).
These are a bit more temperamental than most the species we've met so far.
M. louisiae (sometimes regarded as a subspecies of M. hutchinsoniana). Very small plant with whitish flowers and hooked spines.
M. yaquensis clustering with cylindrical brown stems that break apart easily. Flowers pale magenta.
Tall, cylindrical stems with tubular red flowers (sub-genus Cochemiea).
These come from Baja California and like higher temperatures than most Mammillarias. They're also prone to splitting if you start watering them too quickly in the spring. Most species have hooked spines, which makes it easy for them to get pulled out of their pots.
M. poselgeri is the commonest of this group. It has greyish stems up to 2m long.
Small plants with large flowers.
This is probably the most interesting group. Unfortunately they're also the hardest to grow.
M. guelzowiana looks a lot like M. bocasana but has huge magenta flowers. M. longiflora is similar with less hair. These should be watered about half as often as other cacti.
M. saboae has brown stems with short white radial spines and huge flowers. M. goldii and M. theresae are very similar and their classification is matter of some dispute. Unfortunately it's difficult to even get the seeds of these species to germinate.
Well that's really only scratching the surface of Mammillarias. Books have been written about them! I hope I've encouraged you to get some and given you ideas for growing them whether you want an indestructible plant or a challenge for your expertise.