Harmless free-living copepods in the aquarium

The vast majority of copepods are marine; they can form up to 70% by weight of marine plankton. In freshwater, copepods get some major competition from the cladocerans (such as daphnia), for a trophic role concentrating the nutritional values of plant detritus, euglenoids and diatoms, algae and ciliates as well as other protists, even some bacteria, and converting them into food for small fish.
 
Copepods in turn can ingest fish eggs and the largest of them can prey upon the smallest stages of fish larvae. They are everywhere in temperate freshwaters, though not so numerous in the tropics; whole orders of specialized copepods are only found deep in the lightless groundwaters.
 
"Copepod" is a biologists' Greek concoction meaning "oar foot," which suggests how they move by frantic rowing actions— but those are their antennae they're using, not their feet. All the free-living copepods have a head shield fused with part of the thorax as a cephalosome, which means "headpiece." Females carry two egg cases, which you'll just make out as a double "tail" if you have a good magnifying glass.
 
Negative aspects. Of the ten taxonomic orders that make up the copepods, about half of them mostly have symbiotic or parasitic relationships with fish species. In fact copepods of one specialized kind or another are parasites of every major animal group, from sponges to mammals. This makes some fishkeepers uneasy when they see copepods of any stripe. Most parasitic copepods are marine, though. Again, the rule to remember: "If you can see it, it's not a parasite." 
 
...Unless it's visibly attached to a fish: the most familiar parasitic freshwater copepod is Lernaea, the "Anchorworm"— not actually a worm at all— which we do sometimes see, attached to fishes that have been raised in outdoor ponds.
But copepods have a more insidious role: they can transmit the minute young of Camallanus cotti, a devastating intestinal nematode. Certain kinds of copepods ingest the Camallanus, which pass into the fish that eats the copepod.
 
Trophic roles. But trying to eliminate copepods in a planted aquarium is as fruitless as King Florestan's attempt to ban all spindles from his kingdom in the tale of "Sleeping Beauty". Most of the noticeable free-living copepods form an indispensible trophic link between phytoplanktonic algae and larger creatures. Copepods feed on bacteria, diatoms and other unicellular protists, including Euglaena. So when a milky "bacterial" bloom (probably mostly caused by ciliates) or "green water" clears up all on its own, you can attribute its mysterious dissipation in part to a suddenly-increased number of copepods preying on the over-abundant resource.
 
"Cyclops."  When we feed copepods to fry, we sometimes still refer to them as "cyclops," (the one metonymic  genus being Cyclops) and we're a little wary, because the larger cyclopoid copepods— they can reach 2 or 3 mm— can be predators of some of the smallest fish fry. But the newly-hatched copepod nauplii are small enough  to be the first prey of the smallest fish larvae.
 
 
 
Links. A good portal to links about copepods is maintained among zooplankton general information by Pacific Biosciences Research Center, University of Hawaii. The Smithsonian National Museum of Natural History has a site with four copepod databases,  "The World of Copepods". To give you an idea of what they look like, there are portraits of copepods at the Micrographia website.