Right off the bat, I want to address everyone who is going to reply and tell me that copepods are great; they're like free food, the sign of a healthy tank, etc. Yes, yes, I know that's the standard line of thinking.
But like a lot of things in this hobby, some of the minutiae is often overlooked entirely. There are so many people who will get new fish and insist on running a strict quarantine for weeks, or get new plants and quarantine and dip for snails, yet have no concern for those tiny cyclops that you can barely see (and can't kill...really, they're almost invincible).
Here's the thing. Cyclops are intermediates for a number of really, really annoying parasites. Nematodes, flatworms, and potentially others. In Africa, they spread Guinea Worm (which is an absolutely disgusting human parasite that grows into a 3 foot worm that has to be physically pulled out of a boil on your body). I know, that has nothing to do with our aquariums, but hey, at least it got your attention for the next part
More relevant to our hobby: They spread callamanus worms. They also are what spreads tapeworms.
For people who spend a ton of time trying to treat callamanus worms, only to have them mysteriously come back later... well, if you have cyclops in your water, they eat the callamanus larvae, and the fish eat the cyclops and develop the worms. Unless you eliminate the cyclops entirely, this will ALWAYS be standing in the way of getting callamanus out of your tank. Yes, there is one species of callamanus that skips the copepod host entirely, and if you have those, then the copepods are neither helping nor hindering. But...cyclops also are what transmits tapeworms to fish. Same problem with that one. And they're just one more variable for disease, so they're absolutely not the "harmless" critters like people like to think.
My display tank is currently copepod free. I really don't want to introduce them. The val. I received from Aquarium Coop last week is absolutely run over with detritus worms and cyclops, and I have tried everything to eliminate the cyclops in the quarantine tank with no success. It's like these things are invincible. And now I'm feeling like I'm just going to have to toss it and try ordering elsewhere in hopes that I don't get cyclops hitchhikers.