Recommended Insulation For Finished Basement
I finished my basement a few years ago, and I did a lot of research before I began.  The code here (in Ontario) says you need R-12 with batt insulation, a vapor barrier, and tar paper behind the batts but only, I think, 3' below grade.

From everything else I read, this is the wrong way to do it.  I should also mention that when we had the house built in 2006, it was insulated exactly like this, just without drywall in the basement.  I decided to take off the vapor barrier and take out the batts, and there was already some fungus or mold starting to grow on the basement walls behind the batts.  My opinion is that the code is wrong.

There's a home improvement guy around here named Mike Holmes, and not everybody likes him, but he's generally all about "doing it right".  He's been advocating spray foam, or in lieu of that, using XPS.  I also came upon a website called Building Science.  It had some good information published comparing batts with vapor barrier vs. spray foam or XPS, and they clearly showed the foam better.  They also gave a pretty good explanation of why...

An effective "air barrier" is more important than a vapor barrier.  Spray foam, or very-well-sealed XPS is an effective air barrier, so humid air from inside can never contact the cold basement wall behind it, so condensation can't form.  The foam is also moisture resistant.  The air can only contact the top of the foam, and that's at internal room temperature so it won't condense.  Also, the closed cell nature of the foam will allow moisture in the wall to (very slowly) move towards the inside, where it will evaporate into the room.  For this reason, they pointed out it's important to not have a vapor barrier on top of the foam.

The idea is: concrete is wet, and doesn't mind being wet.  The foam has to tolerate wetness, and block humid air inside from contacting anything below the condensation point.  Allow the wall to dry to the inside, to prevent moisture from building up in the wall.

I opted for spray foam, including up in the headers, which saved me a huge amount of time.  They were done in 2 hours.  The main thing with spray foam or XPS is that you need to cover it with something that has a 15-minute burn rating.  Typically this is just drywall, but you wouldn't be able to leave foam exposed.  I have drywall walls but a suspended ceiling in the basement, so the spray foam up in the headers isn't protected, so the inspector had me put Roxul insulation overtop of it, to act as a 15-minute fire barrier.  He did say that the code still technically requires a vapor barrier, but I disagreed, we had a short discussion, and he basically said, "sure, OK."  

I also used 1" of XPS on the floor, sealed with tuck tape, and then plywood over that.

That was about 4 years ago, and I'm very happy with the result.  It's a comfortable space.