Common HOA horror stories often involve landscaping rules. HOAs can be very picky about what plants you can have in your yard. Some demand that all front yards have a certain type of grass, which can be difficult to maintain in some climates. There are also issues with parking enforcement. I know of an HOA that towed a homeowner's car from their own driveway because they thought it was an 'eyesore'. And communication problems are a big one too. HOAs sometimes don't communicate well with homeowners about upcoming changes or events, leaving homeowners feeling blindsided.
One common HOA horror story is strict and seemingly arbitrary rules. For example, some HOAs have rules about the color you can paint your house that are very limited. Homeowners might be forced to use a particular shade that they don't like. Another is overzealous enforcement. I heard of an HOA fining a homeowner for having a small flower pot on the porch that they deemed 'untidy' when it was actually a nice addition to the home's appearance. Also, there are issues with high fees for little in return. Some HOAs charge a lot but don't maintain the common areas well.