Blackworms (Lumbriculus spp). Since Lumbricus is the common earthworm, Lumbriculus, then, should be the "little earthworm." Though it's cute, the scientific naming is a bit misleading; Lumbriculids actually comprise a wholly separate order (Lumbriculidae) of the Oligochaetes; in other words, they're annelid worms, as much as earthworms are, but as different from earthworms as they both are different from tubificids. Three distinct orders of annelida, the segmented worms. Lumbriculus variegatus, the "California blackworm" of aquaria, is actually three cryptic species, morphologically indistinguishable.
Blackworms as fish foodseem to be endemic to the US. Here fish eat blackworms greedily, but they are too rich for a diet staple; blackworms every third or fourth feeding might be a good regime.
Blackworm fears. Nevertheless, blackworms are very often confused with tubificids (Tubifex and its allied species) and scorned with equal disgust by many otherwise well-informed fishkeepers. You may be told that blackworms "transmit diseases" or, with a precision that sounds even more authoritative, that they "carry an intermediate stage in a tapeworm life-cycle," a possibility with wild-caught tubificid worms. Biologists who know blackworms told me, when I asked, that the response to that tale is "No:" see Dr Drewes' statement below. Joe Gargas (at the killie-talk mailing-list) sent some to a lab for examination and received a report that blackworms do carry their own characteristic co-evolved parasitic nematodes, as all multicellular animals do, but these can't be passed on to fish. Still, blackworms are dissed as "stinky" and suspect, even at that bastion of good fish information TheKrib. Randy Carey mentioned that he inadvertently froze blackworms once, in a metal container in his fish fridge. He thawed them out, and immediately fed them to a number of fishes: still, almost all the fishes died over the next few days. Moral: blackworms must be alive. But so must lobsters and mussels and oysters, if you want to eat them safely. It seems the troubles with blackworms themselves come from mass die-off in anaerobic conditions and from feeding dead blackworms to fish.
Keeping blackworms. So keeping them alive is crucial. Blackworms do best in darkness, and their metabolism slows if you keep them cool. Blackworms need access to air to be alive when you feed them to fishes. I keep them in a cool room in a wide white ceramic dish in enough water just to keep them covered; a refrigerator would be better, but you know how people are about worms in the household fridge. No lid: lots of available water surface provides lots of oxygen. I have unhappily drowned them in warm weather in water that was too deep. Every morning at least, evenings and mornings when I have a concentrated mass of blackworms, I pour the worms off into a jug and flush them, not too roughly, with tapwater. I let the water gently break up any dense balls of blackworms each time. Good worms sink. Dead blackworms turn white. Bad ones, if there are any, float, and I pour off the white floaters, as well as some worms too flaccid to get a grip on their fellows. The temporary pulse of chlorine is okay for blackworms, bad for surficial bacteria; kept for more than a few moments in chlorinated water, the worms show their alarm by attempting mass escapes up the sides of their container.  Then I scrub out their dish. No soap, no bleach, I just scrub it. Finally I barely cover them with chlorine-free water dipped from a plant nursery. If you have some low levels of copper in your tapwater, blackworms may do better in water that's been passed through a Brita-type activated carbon filter, or a narrow strip of PolyFilter that you've kept rolled up tight and stuffed into the tube of a large plastic funnel. 
Telling blackworms from tubifex. You may want to confirm that your worms are Lumbriculus. Blackworms swim; tubifex don't. If you gently touch a blackworm's front end, it can flip in half a second and reverse direction. A gentle poke at the rear end will send a blackworm agilely swimming away. Dr Charles Drewes' article "Helical swimming and body reversal behaviors in Lumbriculus" gives you the details of this characteristic blackworm behavior. Tubifex don't have an escape response like this.
Feeding blackworms. A well-fed worm must be more nutritious than a starving worm. Tom Miglio of Brooklyn Aquarium Society sprinkles newly-arrived blackworms with a light dusting of dry yeast. I feed blackworms the cloudy squeezings of a sponge filter, and they clear their water within a day. Blackworms will clear strands of Java Moss of detritus and algae, leaving it fresh and bright green again. I've taken to leaving a loose mat of Java Moss in their tray, and my impression is, that they stay in better condition and I rarely wash away a dead one now. I've occasionally fed a slice of blanched zucchini to blackworms without trouble. Sometimes I leave the base of an asparagus stalk in the blackworm tray to feed the worms. It's been blanched and usually it's spent a couple of days in the aquarium (asparagus is not the favorite vegetable), softening. The blackworms cluster round the two ends and eat their way inside. So—as far as the gut bacteria they carry (a widespread uneasiness that I don't share)— at least I know what these blackworms have been eating.
There's a neat blackworm keeper that I don't have which consists of a sieve-bottomed container that fits inside the pan. You lift it and the old water drains away. This won't eliminate the dead ones, though. Michael posted at TomsPlace, 10 July 2001, his discovery that if you fill the container with cold water and lay plastic window screen mesh on the surface with the worms on it, then position a light bulb above the worms, they will scramble through the mesh into the water to escape the heat, leaving their dead behind.
I handle worms by lifting them on a wooden chopstick. There's no way to pick them up, even with forceps, without damaging them.
Regeneration. Blackworms take advantage of their segmental annelid body plan by being able to be cut apart without dying; in fact they commonly reproduce this way, by self-fragmentation. This means that when your tetra takes a clean bite, the half-worm that drops to the gravel isn't going to die and decay. Instead it's going to hang on in there till a Corydoras sucks it up. 
Leeches? The other important thing is to make sure that no tiny leeches are lurking among the worms. "Ugh. Leeches. Filthy little devils," said Humphry Bogart in The African Queen. One unpleasant issue with leeches that may lurk among the blackworms is that certain leeches are the vector for transmitting a nasty class of parasitic flagellates, the trypanosomes. (If the name trypanosome is vaguely familiar, it's because malaria is a disease transmitted by trypanosomes.) Insidious trypanosomes in fishes cause lethargy, then bloating ("dropsy"), and death, with no way to treat for them. The tiny leeches among the blackworms are preying upon the worms. I think a fish would eat them, but I'm too squeamish to try.
It's better to keep the leeches out of the food chain altogether. To eliminate leeches, slide the blackworms gently from their current container into another each time you wash them. The little leeches will reveal themselves by clinging tenaciously to the container, using the sucker at one end or the other; blackworms just slide. Out with the leeches!
Blackworm culture. There's a good introduction to California Blackworms (Lumbriculus variegatus) by Dr Charles D Drewes PhD of Iowa State, who gives culturing instructions and praises the worms to biology teachers as instructive lab animals.
 I asked Dr. Drewes about the reputation of blackworms as disease transmitters. I was specifically alarmed that blackworms might transmit the microscopic young of Camallanus, the insidious parasitic nematode. Dr. Drewes replied, "Thanks for your inquiry about blackworms. The answer to your question about Lumbriculus transmitting Camallanus infection is a definitive NO. I have checked with our resident parasitologist who has more than 30 years of research and teaching experience in parasitology and life cycles of parasites. Camallanus is transferred by copepods of several different species, not by oligochaetes. Perhaps, it is possible that your tanks already had a few copepods in them and they "bloomed" which these small invertebrates can do. Or, perhaps the water and residues that worms were in when you purchased them were somehow contaminated with copepods. I have been doing research on oligochaete worms (both terrestrial and aquatic) for about thirty years and do not know of any parasites that are transmitted by Lumbriculus (blackworms). This, of course, does not mean that they cannot transmit parasites of some type. I do know that whirling disease in fish can be transmitted by tubificid worms and that other organisms such as small leeches and even tubificid worms do occasionally show up in bulk Lumbriculus that are sold. "Here is what I would recommend to help minimize problems: When Lumbriculus are purchased, do not just throw some into your fish tanks. Rather, immerse and rinse them in spring water (dechlorinated tap water) in a shallow white-colored pan. Use an eyedropper to remove and discard decaying worm carcasses, damaged worms, or alien life forms. Withdraw the intact lively Lumbriculus worms and use them to feed your fish. Discard (flush) damaged or worms whose identity or health is doubtful. I know this is tedious, but with a little practice, it can be done quickly and efficiently and it may save time, expense, and headaches. "By the way, one good way to clearly prove that a worm is Lumbriculus and not a tubicifid (tubifex worm) is to to lightly tweak its tail end while it is freely crawling underwater. If it quickly attempts to get away by swimming a short distance using helical twisting movements, then it is definitely Lumbriculus. If it is unable to swim, then it is either a messed up Lumbriculus or a tubificid worm—and discard it. Tubificids cannot swim.
"By the way, I would always check with pet shop owners to find out when their shipments of Lumbriculus come in, so that you can get the freshest ones possible. They usually store them in the refrigerator and if they have been in there a long time, they may be full of dead worm carcasses and really stinky. I certainly would worry about bacteria, fungi, and toxins that could build up in a half-dead masses of worms!
"I have raised my own Lumbriculus for many years in my laboratory. I use them for teaching and research. They are very easy and cheap to raise and require little care. I will mail culture instructions to anyone who asks. Please feel free to share this email information and website with whomever you wish.
Good luck and thank you, (Prof.) Charles D. Drewes"
"California blackworms" are being farmed under controlled conditions in fishfree ponds and distributed through the web in wholesale quantities, which is to say by the pound,  by Aquatic Foods, Fresno CA; these people supply most of the other sources you'll find for blackworms. I haven't used them yet myself, because until very recently I've been able to buy them, thimbleful by thimbleful and at glamorous prices, at my late, lamented LFS. The chain stores don't carry blackworms.