Yes.
Depends on what apps you use. Its necessary if you want to hand write any notes or use any art apps seriously you need one. The one I have is very responsive, though hard to be precise with since its got such a large tip (has to be large).
Its also nice to use when you've got your screen extremely clean and don't want to get fingerprints on it for a bit, and of course it lets you use it with gloves on if you ever have the occasion.
I'm considering buying the jot pro and trying that, it has a clear disc as the tip so you can be more precise. $30 though so Ive held off so far.
If you are just kind of interested I wouldn't buy one overpriced in store for $15 or $20, but you can get the same thing on Amazon for $5 or so and its nice to have around even if you dont use it that much. Don't buy the .50 cent ones that often arn't responsive.
as for Apps.... Ive used it in note taking apps, mainly to do little sketches combined with text (my handwriting sucks I stick to type) and such for more fleshed out idea notes. And full fledged art apps like art rage, sketchbook pro, etc. There are a few slow paced games Ive used it for but thats never really needed.