UPDATE: I did research this method before publishing this 2 years ago and found that using the plain black and white papers generally were fine because of the type of inks they used. I also found that it best to stay away from using anything printed in color. If you are ever unsure just contact your newspaper company and they should be able to tell you or find out. Here is a link that I found that explains it a little more.
Using Newspaper as a weed barrier in a garden
Use 6-10 layers of newspapers with shredded leaves, straw, and/or coffee grounds on top, its organic so it will break down in the soil and is better for the soil than weed cloth. No need to worry about having too many layers of mulch, more is more often than not better.
I've found that with the extra nutrients and moisture retention from the thick mulch the plants will grow bigger and crowd out most weeds anyways.
If you're gardening with rows of vegetables you can change to using wide beds (2 ft wide if against a wall, 4 ft wide if there are paths on both sides). This will also reduce the amount of weeds, since groups of plants reduce the area for weeds to grow in.
When planting in rows weeds can grow on both sides of the row, so the weed circumference to planting area ratio is large. When planting in wide beds the weed circumference to planting area ratio is smaller, so less weeding is needed.
What Paper to Use
The coarse paper of the standard part of the newspaper is suitable for use as mulch. Do not use the slick or glossy advertising inserts often included with newspapers. This is the same portion of the newspaper that can be recycled.
Wetting the Paper
Wetting the newspaper helps create weight that will hold the newspaper in place and allow it to mold to the ground. Place a minimum of five layers of newspaper across the ground, and cover them with mulch. Stagger placement of the pages so the seams of one layer are covered by the center of other layers. Shape the newspaper mulch around the desired plants in the garden.
Covering the Paper
Newspaper is not the most attractive form of mulch available and can blow away once the initial moisture dries. Scatter leaves, sawdust, hay or straw across the wet newspaper mulch. Spray these with a garden hose to hold them in place. Using organic materials as a cover for the newspaper mulch allows both materials to be incorporated into the soil at the end of the growing season.
Working it Under
A rototiller breaks up the weathered newspaper and works it and the cover material into the ground, where it decomposes. Accomplish the same process with a garden fork or shovel with a little more sweat and effort. Work the newspaper mulch and cover into the ground as soon as the growing season is over to prevent the materials from blowing in the wind.