As others have said, cichlids are a really diverse bunch. Even within the African Rift Lakes they've evolved into "endless forms most beautiful" as Darwin once said. That said, there are some common threads.
-Territorial: Every cichlid that I know of is territorial, from the tiny banded shelldweller to the massive peacock bass. So when keeping them you need to be aware of what kind of territory that fish prefers, how much territory it will take, and how fiercely it will defend it. As an example, look at angelfish. They prefer the upper water column and take a fairly large territory but tend to be relaxed about it outside of spawning. Now compare that with ram cichlids who prefer the bottom of the tank and are a litter more fierce guarding their territory but also don't take as much. You can actually mix the two because they have different territory needs. Good strategies for dealing with cichlid territorialness are putting in lots of cover and "landmarks" in the tank for natural territories to form and introducing cichlids all at the same time after all the other fish have been introduced.
-Parental care: This goes hand in hand with territory. Cichlids all take care of their offspring, or at least they are supposed to (some longtime captive bred staples like angelfish have lost that instinct). Most of the common cichlids in the hobby form pairs, but some form colonies (like certain shelldwellers), others breed in trios (apistos), and so on. Then these pairs, or at least one parent, will fiercely protect their fry. This is generally bad news in a community tank, so it's something to be avoided if you can sex your fish.
That's all I can think of for general cichlid characteristics without getting into the actual taxonomic distinctions.
