This is used at the end of a sentence and contains a variety of meanings. We will look at it as a question tag.
As a question tag: don't you... isn't it...
あなたはにんじんが嫌いですね。 anata wa ninjin ga kirai desu ne. You don't like carrots, don't you?
その映画はとてもいい映画だったね。 sono eiga wa totemo ii eiga datta ne. Don't you think that was a good movie?
今日は暑いですね。 kyou wa atsui desu ne. Today is very hot, isn't it?
If you want to use ne as a question tag, it helps to nod your head, or change the inflection to let the listener know you would like a response. It is usually used when the speaker feels fairly certain his listeners agree with what was said.
A very useful phrase for whenever something good happens is:
いいね。 ii ne. Isn't that great!