Certifiable.
or Mental.
Cookie-cutter.
I dunno if that quite counts. If you hear a person described as healthy, you don’t assume that means they’re fat.
I think ‘‘curvy’’ is a good example. Even if I weren’t fat, I would be curvy, but I would never describe myself as such due to the negative connotation.
‘‘Community organizer.’’ I will never forgive Sarah Palin for that cheap shot. That bitch wasn’t just insulting liberal do-gooders but pretty much every grassroots movement that generated success for the Tea Party so they could support idiots like her. The conservatives by their own admission modeled their own grassroots movement off of the great liberal organizer Saul Alinsky, and she’s gonna throw shade like that? Hell to the no.
He’s special
Being cynical (in my opinion).
I called someone cynical the other day and they took it as a bad thing when I meant it as a compliment (I’m cynical myself and find it a good thing to be, at least a little bit).
The word consequence has a neutral denotation, i.e. “A result or effect of an action or condition.”, but its connotation is usually for a negative result of an action.
Meeting really just means more than one person getting together to discuss something, but anyone with any time in the corporate world knows it as a synonym for “waste of time I can’t sleep through”
I will never forgive liberals for the vicious, idiotic assaults on her (like yours) that STILL continue.
When a female describes herself as “curvy” it usually means she’s a sphere.
Conservative.
Virgin.
But really, I think that a sufficiently skilled orator or writer (and I am neither) can make pretty much any phrase positive, negative, or an insult.
Graphic.
I’m wondering if the word “retarded” is heading this way, too, although could one argue it was always somewhat negative?
Exceptional. When I was in grade school, in the span of a few years “exceptional” went from meaning advanced to slow.
Agenda. As in “gay agenda”. Why is it a bad thing to fight for equal rights? 
Also: Tea Bag.
[I make no connection between the two BTW. :)]
When a man describes a woman as ‘curvy’ he means she’s got big tits.
In the UK we do not see ‘liberal’ as pejorative. ‘Liberal’ with a capital ‘L’ is often used as a synonym for weak minded wishy-washy; particularly in the press.
69? 
(Well, it’s not negative if you enjoy it.)
Don’t know if this is exactly on-topic, but the word “modest” is often used ironically, when someone is being boastful.
Discrimination-Used to imply someone who could make distinctions and of sound judgement
Puritan-Refers to the movement to reform the Church of England in the 17th Century not hysterical, McCarthyite Victorian moralists
Fagged-In the sense of “I’m fagged out”.
It used to just be a clinical term, then it became an insult. But really anything you replace it with like “special” just winds up getting used the same way so they should quit bothering to find new terms.
Ok, I give up. Which word in this example sentence is used negatively but really has a neutral meaning? Because there’s no way you’re serious, right?
My word is atheist. It should be just a descriptor of a person’s position, but it’s said with such venom that it’s now considered almost communistic or something to be one in certain locations.
Maybe. You imply that the majority of “negative” words carry their negativity by denotation alone.
In fact, as this thread seems to demonstrate, I would say that just as many–if not more–“negative” words acquire that negativity through connotation, by historical context. That’s the very essence of language.
The pragmatics of connotation is ever fluid, because a word like curvy, for example, is part of a larger social discourse, and can’t really be singled out in isolation as having a renegade “negative connotation” all on its own.