Dumbledore was a human and by increasing his life span, he was defying nature like Voldemort. Why wasn't there any curse or negative effects from that?
One major reason members of the Wizarding world live longer than normal humans is very simple: they have much better medicine than we do. We see Madam Pomfrey completely regrow Harry's arm bones from nothing, at one point, and she's a school nurse. I imagine the things that commonly lead to death of old age in humans (cancers, heart disease, neurological conditions) really pose no difficulty to magical medicine, especially at someplace like St. Mungo's.
As an aside, this can be seen in our world, too. If you look at the life expectancy of the Dark Ages (around mid 30's on average), we have made much progress towards a Wizarding lifespan. The medical community has been postulating for the past decade that if we could overcome a few of the more troubling diseases we commonly face, then we could live lives well over a hundred years long.
Dumbledore's lifespan isn't unnatural for a wizard. Other wizards who have naturally lived to a similar age to him or older include:
- Grindelwald was his childhood friend and doesn't die until Deathly Hallows when Voldemort kills him.
- Griselda Marchbanks was his N.E.W.T. examiner -- so she's presumably significantly older than him -- and she still serves on the Wizengamot and does N.E.W.T. exams as of Order of the Phoenix.
Presumably wizards simply live longer than Muggles.