They are prejudiced against Muggles, Muggle-born witches and wizards, and witches or wizards with close ties to Muggles. They typically use fear and violent methods to maintain control over the Wizarding World. It should be noted that they are only a portion of the forces Voldemort had at his command, though they were used the most in the novels and films.
They consist almost entirely of pureblood families, and have much support, both financially and personnel-wise.
Death Eaters are indicated by a Dark Mark (a magical tattoo of a skull with a snake coming out of the mouth) on their left forearm.
Death Eaters appear in a great deal of Harry Potter fanfiction, though this is hardly a surprise. They are almost always given antagonistic roles, and will sometimes only be there as Generic Troops, serving little purpose other than to make the battles fiercer. They are depicted as cruel and merciless, and cowardly towards their master. Displaying them as woobies is in poor taste, as is making them appear completely useless, as many of them are fully grown, battle-hardened wizards (though their pride can be their greatest weakness, and in canon regularly get trounced by schoolchildren).
In badfic, they are depicted as your basic 'evil guy's henchmen', and while this is not an entirely bad thing (as they are evil), it does tend to make them so generic, they are sometimes reduced to mere plot devices. Need a good start for an angsty hurt/comfort fic? Death Eaters kill/attack/rape a character or their family, and make way for the mush. Need to show off how awesome Cool!Competent!Notwhiny!Harry is? Have him (and very rarely others) get into multiple battles (or sometimes just one really big one) and have them fall by the dozens. Want to make Dark!Evil!Slytherin!Harry more intimidating? Simply have him kill Voldemort and the legions of evil shift to his command! (Or have him make his own dark followers that completely trounce the Death Eaters!)
Like the problem with Sith in the Star Wars continuum, some Mary Sues (or even just fangirls portraying canon Death Eaters) think it would be really cool to be a Death Eater because they're so dark and edgy and goffik—often trivializing that they are brutal murderers and torturers.
It should be noted that they do have reasons and motivations for their actions in canon (no matter how evil or selfish) as well as diverse backgrounds and personalities, and making them into one- or two-dimensional throwaways is a charge.