I'm so glad you asked this question. I have wondered this myself and it prompted me to actually do the research!

A Little Background

A few years ago I started baking all of my cookies on cookie sheets covered with parchment paper. I got hooked because my cookies would evenly brown and clean up was a cinch. However, I didn't like to continually "waste" parchment paper. So, with Martha Stewart's urging I bought myself a Silpat. This was before the silicone craze when there was only this one brand to choose from. No colorful silicone muffin and bundt molds, just this plain brown sheet made of fiberglass covered in silicone. 

What is Parchment paper made out of?

Parchment paper is actually "a sheet of paper impregnated with silicone, which makes the paper grease- and moisture-resistant as well as relatively heat-resistant. It is commonly used to eliminate the need to grease baking pans--allowing, for example, repeated batches of cookies to be baked without regreasing the pans--and it can also be folded to make moisture-proof packages in which foods can cooked or steamed."(1)

Parchment is typically made with bleached white paper. However it can also be found made with unbleached brown paper. Since the bleached paper might contain toxic dioxin, it's better to use the unbleached parchment paper if you use it. (1)

What are Silicone baking sheets made out of?

Silicone baking mats simply "replace the paper substrate with, in most cases, a finely woven fiberglass mesh that helps the silicone to keep its shape and prevent tearing."(2) They are easy to clean, take up little space in the cupboard, and are completely reusable. 

Will the Silicone leach into my food?

Although this is a completely manmade product it is certified by the FDA, NSF and is certified Kosher. There should be no plastic or chemical type of smell when you use your silicone mat. If there is, return it to the store or call the manufacturer for a refund.

What brand do you recommend?

There are many brands, colors and styles to choose from in the world of silicone. However, with one exception (a muffin mold I just had to try from IKEA) I've steered clear of anything but my, made in France, Silpat. I have two reasons for this. #1. I don't trust colors. To get those bold brilliant colors such as red, blue and yellow lead is often used as an ingredient in the coloring. #2, I know how the French feel about their food, and how it is prepared. I trust them to know what they are talking about and I trust that they're not going to use cheap material that is going to leach something into my delectable treats.

When it comes to cooking equipment price often equals quality. Silpats generally run around $20-25 while off brands can be had for $10-15.

Turn's out Martha Stewart was indeed correct, a Silpat baking sheet is indeed "A Good Thing!"

For more information on silicone baking sheets:

(1) http://www.dld123.com/q&a/index.php?cid=97

(2) http://itotd.com/articles/303/silicone-baking-products/

http://en.wikipedia.org/wiki/Silicone