ね at the end of a sentence

Why do Japanese people always tend to end their sentences with ね? Does the ね have a specific meaning or is it one of those set phrase kind of thing? I know my host mother always used ね at the end of her sentences and it seemed like she was asking me questions. But I also heard other people use it and it didn't really sound like they were questioning each other. Could someone explain this concept that totally baffles me? Could you also put it into a sentence and try to teach me where and how you are supposed to use ね?

Ne at the end of a statement of a is usually used to invite the hearer to respond to a statement as in:

Mae ni mo doko ka de atta koto ga arimasu yo,ne? Rising tone.
(We've met somewhere before, haven't we?)

Also for confirmation. On seeing a fierce looking dog:

That dog doesn't bite,does he?
(Ano inu kandari shinai yo,ne?) Rising tone.

When we talk about the weather or mutual things.

Kyo wa ii tenki desu ne. Falling tone.
It's a lovely day, isn't it?

Denwa bango shiteru yo,ne.
You now my number,right?

Tanoshikatta, ne.
That was fun, huh?

Just think of it as a tag question Ne used at the beginning of a statement is different,though.

Can't it also be used, not as a question, but to soften the tone of the sentence?

Yes, it can.

By the way, here is more on emotion markers (yo, ne, and even the affirmation suffix no da).

thanks cricket and glenn, the emotion markers webpage was a big help.

Yo (ne) isn't only for expressing opinions or beliefs, though. In a case like this, appended to a new piece of information it acts to add moderate emphasis. And I tell you (besides rent) there's also transportation, electricity, gas, water, phone utilities and clothes you'll need money for, isn't that right ?

日本に住む時の生活費ですが、家賃が６万円としてもそ れだけで年間７２万円かかります。
食費を１日１０００円としても年間３６万５千円かかり ます。
電車代も必要でしょうし、電気代、ガス代、水道代、電 話代それに服も要りますよね。

The use of "ne" as a softener for presumably neutral sentences like the one below still get me, though. At first I thought he was reminding me of something I should have known but then realized it may come more from a sense of personal modesty -- listing all the places you'd been could come across as braggadocio, even if was only three.

友達の車に同乗させてもらって、福島、宮城、山形に行 っていましたね。
最近は行ってませんけど。

Yeah, sometimes the use is a bit hard to categorize. I know that there are other uses, but I was giving that link just to get Genius started, because he seemed to not know anything about it.

Also, yo can be used to soften imperatives. I.e. yasai o tabero is harsher sounding than yasai o tabero yo. It seems to be a paradox, but it is supposed that the reason for this is that yo gives a more conversational feel to the command, rather than just a direct order.