The Fourth World are those collection of characters based on either Apokolips or New Genesis. Throughout my years of reading comic books I have found these to be some of the least engaging characters in comics. Not only one, but two, big DC crossovers have been sort of ruined by an over reliance on them (Legends and Final Crisis). Here are a few reasons that I am not such a big fan.
Complete Lack of Imagination in Their Names and References to Stuff on Earth
Darkseid has an ominous sounding name, and actually sounds intimidating, but why spell it the German way? Doesn't this sort of all into the concept that all Germans are villains? DeSaad the sadistic torturer? Kind of like the Marquis de Sade from where we get the term sadism. Artemiz the bow using assassin? Well the connection to the Greek God Artemis is pretty clear. Orion? That is not even a play on the writing of the name, just a direct rip-off. On the other hand you have a few which are completly lacking inspiration - Lightray and Highfather? those aren't names as much as descriptions. There are a few names which I like - Mister Miracle, Granny goodness, Kalibak, but so many of the rest are uninspired.
Poorly Defined Reasoning for Hating Earth
Darkseid controls his own world with an iron fist and has been successful through the years of publication history of occasionally being able to destroy New Genesis. I never found out his fascination with Earth though. In some senses I guess it could comprise some sort of personal vendetta against Superman or other hteroes who have helped stop him over the years, but mostly he has no real reason to hate Earth any more than any other planet, yet he is never shown with even the slightest bit of interest in those either. He is constantly dividing his forces for differrent battlesgrounds which weakens his overall effort.
No writer will ever be able to write an adequate explanation for what the anti-life equation is
This has been hinted at over the years and sometimes actually defined but it has been either represented as a ball of energy available behind the source wall or just a sequnce of words which somehow represent the opposite of life. That equation is "loneliness alienation fear despair self-worth ÷ mockery ÷ condemnation ÷ misunderstanding × guilt × shame × failure × judgment" but I don't see how knowing that allows Darkseid infinite power.
Unlike Earth the planets of New Genesis and Apokolips have only one belief system as opposed to the hundreds there are on Earth. No one on new Genesis has come up with the concept of polytheism or something more internal like Eastern religions. Granted they have a pretty obvious example of their gods on a day-to-day basis, but it still seems strange that no one has thought of anything else. In fact for how many times Superman has intervened to save the worlds you would think some would regard him as a god.
So what really makes these guys gods anyway? Granted Darkseid is pretty tough and can usually outfight Superman, but there is really nothing which makes these characters gods. DeSaad is the god of torture? Granny Goodness is the goddess of feeding porridge to children? The only one of these which ever showed any orginality was Mister Miracle, the god of escaping, but I don't know who would pray to him (other than thousands of office workers on Friday afternoon.) The gods don't really have a traditional god-like role either as they have no real temples or oracles.
A general lack of continuity
Darkseid and his minions are usually just thrown in whenever the is no need for a superpowered bad guy with no real reason for doing what he is doing (for instance the already mentioned miniseries Legends or Final Crisis.) Compounding this is that he acts differently from time to time. Once in the Birds of Prey he didn't care that a group of heroes had invaded Apokopolis. On the other hand another time when the Suicide Squad invaded he got pretty upset. Other times he has tortured Wonder Woman for the knowledge of where the new home of the Olympian gods is, though what he was planning with that information was also not clear, nor did he ever really try and figure it out again afterwards.
I am sure there are fans out there who will want to defend the whole concept. I am not really opposed to it, it just that it is not very compelling. As with any in comics I am mostly here for the writing, so when the writing resorts to cliches and unoriginality (as it most often does with the fourth world) it leaves me wanting more.