So I saw a post one of my blogrolls (I have a few hundred I read so apologies for not remembering which one) and saw a post about spun newspaper. I decided to give it a quick go and realized that it is AMAZINGLY easy and pretty fun (but a bit messy on the fingers.)
I just spun this bit with my drop spindle...

Oh yeah and its really strong stuff too.. I was knitting with it for a bit and it didn't break or tear.

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I wanted to add a quick tutorial so I can show how easy it is.
Supplies:
Spindle (haven't tried it on the wheel yet..)
Newspaper (one Sunday paper would probably be a great start)
Scissors

1.) Take one sheet from paper (such as the front/back page) and keep it folded in its natural fold. Then fold into quarters. (pictured above folded in half)

2.) Cut into 1/2" - 1/4" strips.


3.) Twist your first strip with your fingers until it is twisted about halfway (6-10 inches)

4.) Wrap this hand-twisted part around the base of your spindle (instead of using a leader yarn)

5.) Start spinning in the direction you twisted your paper using your thumb and first finger to guide it. (See where the triangle is under my thumb? It is easier if you hold the twist under that triangle rather than letting it fold and twist up.)

6.) Now to add on your next strip you need to leave 1" -1&1/2" at the tail.

7.) Place your second strip on top of your first like in the picture.

8.) Start spinning while holding the strips together.

9.) And continue onward!!

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And you can make a thinner "yarn" by cutting the strips of paper thinner! Image posted here :
http://www.craftster.org/forum/index.php?topic=203907.msg2178479#msg2178479