"Non ne voglio più."

Translation: I do not want any more of it.

[dnovinc]

"I don't want it anymore" should be accepted.

EDIT: It shouldn't be accepted check Nitram15's comment :)

[Nitram.]

No, it shouldn't be accepted. "i don't want it anymore" would be: "Non lo/la voglio più"
The pronoun "ne" has a meaning "of something", just think of this conversation:

English:

• Do you want some of these apples?

• No, thanks, I don't want any of it.

Italian:

• Vuoi di queste mele?

• No, grazie, non ne voglio.

What you want to say would look different. Look at this conversation:

English:

• Do you still want this apple?

• No, thanks, I don't want it anymore.

Italian:

• Vuoi ancora questa mela?

• No, grazie, non la voglio più.

So, remember: "ne" can only replace structures with "di+anything". And it can stand in idiomatic phrases like "andarsene", for example, which means "to leave", and is conjugated like this:

(io) me ne vado

(tu) te ne vai

(lui/lei) se ne va

(noi) ce ne andiamo

(voi) ve ne andate

(loro) se ne vanno

[olgapo]

thank you, nitram15, yours was the best explanation!!!!

[Lloydo3000]

I'm quite sure this could also be "I don't want (any) more of them." Should I report it?

[AlanChusuei]

Yes please! I wrote this too

[hoelt]

So what is ne? It?

[naten]

"ne" is a pronoun meaning "of it", "about it", "from it", "of them", etc.

http://italian.about.com/library/fare/blfare167a.htm