Round millipedes, as well as the pill/ball millipedes, are in general light-shy, fossorial creatures that will spend much of their time underground. Polydesmids on the other hand tend to be much more surface active, and will rarely burrow for long stretches of time except when molting or laying eggs. The platydesmids are more cryptic by nature, and will rarely be seen on the surface en masse, though being blind they can often be caught on the surface exploring.
Whatever millipede species one keeps, it is important to avoid digging up specimens when they go underground. This is especially a problem for neophytes, who become anxious as soon as the specimen(s) are no longer easily visible. Remember that millipedes are fossorial in the wild, and burrowing behavior is perfectly normal and to be expected. Millipedes burrow to molt and to lay eggs as well; unearthing them in either case can be deadly, as numerous contributors can recount multiple times when specimens and eggs were killed due to ill-timed digging.
Should one's specimens go underground, the best thing to do is to wait; if they do not surface within six months, it may be worth gently probing the upper layers of the substrate to see if the specimens have died. Keep in mind there are reports of specimens going underground for over a year before resurfacing, and there is an inherent risk in digging of any kind. If any individuals are found alive, cover them back up and leave them, especially if they have just molted or are about to molt, in which case they will appear dully colored, similar to when snakes go "opaque" before shedding. If they are in the process of molting it is best to leave them exposed to prevent the substrate causing problems with ecdysis.
If any are found dead, there is a good chance other specimens have also perished. If dead specimens are found and a proper care regimen is being followed, it is most anyone's guess as to why, though individuals that were bought in poor health or that were very old often tend to die in such a manner, and such losses are not reflective on a keeper's ability.
Most millipede species will surface sometime after the room lights have gone out to explore the enclosure and feed upon whatever is on the surface. Night is usually the best time to view them because of this, and often they will be seen clustered around whatever supplemental food was offered in the daytime. Keep in mind however that unless one is using a red lamp to see them, many species will begin to burrow away once a light comes on.
Some species are active during the daytime (notably Chicobolus spinigerus and some poly-and-platydesmids species), and many species can be seen in the mornings on the surface, either curled up in coils, twisted into odd convolutions to groom themselves (this will look like the millipede is trying to eat its own body sometimes), or wandering about in search of food. Most species move rather slowly, and will only start to "run" if touched, exposed to light, misted, or otherwise disturbed. If the enclosure is too dry or there is little-to-no food present, specimens will surface even in daylight and race around the enclosure in search of an escape; with a proper care regimen this should never happen, but if it is seen check the moisture levels and whether or not the substrate needs to be replaced.
Another common behavior when the substrate begins to get too dry is for specimens to sequester themselves at the bottom of the enclosure, where the majority of remaining moisture will be found. If the substrate appears to be dry and specimens have not been observed in sometime, adding water to the enclosure will help ensure no specimens desiccate. Most juliform millipedes will generally never exude their chemical secretions (powerful concoctions of poisons, including cyanide and benzoquinones) unless disturbed, while some species will do so at even the slightest breath of air. A small selection of species cannot be provoked to release their toxifabricants by physical disruption. This includes the majority of the pill millipedes.
Polydesmids are capable of poisoning themselves in poorly-ventilated enclosures due to their proclivity to exude their secretions constantly in small amounts.
While many millipedes will explore new branches, logs, etc. that are added to the enclosure, millipedes are not like many vertebrates (or even invertebrates for that matter) in needing stimulation or "play time". As such handling and providing "toys" is solely for the pleasure of the enthusiast, and provided it is done safely, has no negative affect on the millipedes.
When handling be sure to always keep the specimen(s) no higher than their body length above a surface, and they should always be handled over something to cushion a fall, such as a clean blanket. Handlers should also wash their hands before and after holding specimens, to prevent chemicals and other products from harming the millipede during handling, and to prevent any chemical secretions from the millipede from traveling to sensitive parts of the enthusiast's body, such as the eyes. Some species have such powerful secretions they are capable of inflicting painful chemical burns and potentially severely injuring sensitive parts of the body; for these reasons it is advised not to handle millipedes that are secreting, to put specimens on one's face, or to handle specimens that are known to have especially powerful chemical defenses, or that can discharge their toxifabricants at high pressures (such as members of the genus Salpidobolus).
The exudate of small specimens is generally not harmful on non-sensitive parts of the body, but it will discolor skin a yellowish-brown color for up to several months if it isn't washed off within a minute of contact. Rubbing the affected skin on soil or leaves quickly removes the exudate and usually prevents the skin from being discolored if water isn't readily available.
See the species reports on the family pages for specific behavioral information.