Sentence ending particle. Used either for seeking agreement, or when sharing one's impression with someone else.
Contrary to what big fat header in notes says, there does exist a usage of ね not at the end of sentence. This is similar to English meaningless "like", as in: それで、彼はね、全部納豆がきらいんだよったね。 So, he was all like, "I hate nattou", right. Here the first ね serves only the purpose of engaging the listener more, and just like in English, it can be overused easily.
ね is often used with statements about things that are fairly obvious (the 'classic' example is いい天気ですね。 - "Nice weather, isn't it."). It can (but doesn't always) have a similar effect on a sentence as "I see that..." in English (example from Chrono Trigger, slightly modified to not be feminine): やっと起きたんだね。 (yatto okita nda ne.) I see you're finally up. And mathrick is absolutely right, though that's arguably a different ね. I think of it as being something like interrupting yourself to make sure the other person's paying attention, sort of like interjecting "okay?" or "listening?" into the sentence. Maybe it's just me, but overusing this seems to make you sound girlish. Take this line, for instance (from the song Dreamer -a innocent magical girl-): 街に出かけたら今日も 声かけられた (machi ni dekaketara kyou mo koe kakerareta) でもね実はね私 興味ない (demo ne jitsu wa ne watashi kyoumi nai.) I was called out to [probably closer to "hit on" given the context] again today when I went out into the city But, okay?, the truth is, you listening?, I'm not interested. And just to confuse things more (not really), there's yet another ね. Stick it at the beginning of a sentence (or even as its own sentence) as sort of a demand for attention (another example from Chrono Trigger): ね、いいでしょクロノ？ (ne, ii desho kurono?) Hey, you don't mind, right, Crono?