These words are often connected to violence and abuse, and because of that they have trigger-power: they can make people relive abuse with almost as much pain as the first time. If you have been physically, sexually, or emotionally attacked by someone while they called you a slur, that word may be a damaging one for you to come across, especially in an angry or attacking context.
[list of slurs, trigger warning]
The ones that most people (who I know) can recognize as slurs because oppressed people have said it over and over and over: gay, retard/ed, nigger, jew or gyp (as in to swindle/cheat), tranny, shemale, cripple, slut, whore, fag/got. Words that people do not generally accept as slurs:
Stupid, idiot, dumb -- these words have their power because we devalue people who are neuroatypical: people who don't think in the ways that are valued by mainstream society. They reinforce the idea that to be neuroatypical is to be less-than, much like the word "retard" does. Stupid, in particular, is often used in reference to people who have done something harmful to someone else: this places the responsibility for making moral choices on a person's neurology, and implies that people who may not think as quickly or in the same way are incapable of making moral choices.
derp, that thing where you turn "o"s into "er"s (ermahgerd etc) -- these both get their power from the mocking of people who think slowly or speak differently. They reinforce the idea that to think slowly or speak differently is to be an acceptable target for mockery; to deserve less respect.
crazy, insane, psychotic, wacko, mental, psycho, cray-cray -- these gets their power from the devaluing of people with mental illness. They reinforce the idea that to be mentally ill is to be less-than, to the point of having your rights stripped and your words invalidated.
bitch -- this gets its power from the devaluing of females (and perhaps the devaluing of dogs). It reinforces the idea that to be female is to be less-than. It often is used in the context of rape and thus legitimizes the idea that to be less powerful is to be deserving of rape.
douche, pussy, cunt -- this gets its power from the devaluing of vaginas: if vaginas were respected, not only would the concept of the douche not exist, but liquid that had been in the vagina would be value-neutral. Calling someone a pussy would have no derogatory power. Use of these words as insults reinforces the idea that vaginas are dirty or disgusting.
lame -- this gets its power from the devaluing of people with mobility impairments. It reinforces the idea that to be disabled is to be less-than.
ghetto -- this gets its power from the devaluing of people who live in ghettos. It reinforces the idea that to be poor and/or a person of color is to be less-than.
blind or deaf -- when used to mean "not paying attention" these imply that deaf and/or blind people do not pay attention, or that they are less capable of sensing and interacting with the world.
Note: when I say slur, I mean that an oppressive word is being used in an insulting or negative way -- I'm not referring to self-labels.
To extrapolate and summarize: "does this word get its insulting power from an association with an oppressed group?" if the answer is yes, don't fucking use it that way. If you don't know what to call a person if you can't call them a bitch or a douche, look up 'bad' in the thesaurus (scroll down past the usage notes to find a shitton more). Or consider actually saying what you mean. On that note, for more eloquent and less me-centered examination of slurs: on use of 'lame' 'gay' 'retarded' etc. as insults or negative expressions.
*except for reclaiming: that is, society puts you in a group labeled with a slur, and you self-identify with that as a way of rejecting the stigma. For instance, I have reclaimed the word "fat" and use it as a self-label. I do not ever use it to mean something negative.