Sleeping Pad

Self-Inflating Pads
Most backpackers use a self-inflating, open cell pad. Selecting the length (long, regular or 2/3 length) and thickness is a trade off between insulation and comfort versus weight.

Foam Pads (Non-Inflating)
Non-inflating foam pads are a cheap and lightweight way to get the minimum needed amount of insulation and padding. Their biggest disadvantage is that they aren't compressible like an open cell foam pad so they are extremely bulky. So, if right now you're thinking "Hey, why can't I just use the open cell foam pads like the ones at Walmart for beds and stuff, as a sleeping pad?" then you've just asked a good question... keep on reading.

Open vs. Closed Foam
Open foam, like the kind found in pads for beds, is great for inflatable pads, but not so good for use by itself for a couple reasons:

1) It soaks up water. Since each of the cavities of a closed foam pad are linked together, water moves through it via capillary action, and it thus acts like a sponge (for all intents and purposes, it really is a big sponge). Closed foam pads don't do this, and more closely resemble Styrofoam.

2) It doesn't maintain loft underneath the user. A mattress pad doesn't need to keep you warm (you have a foot thick mattress underneath you after all), and it's purely for comfort. Inflatable pads compensate for this by having a valve which allows air to come in, and can be sealed off to maintain pressure and its loft.

Inflatable (No Foam Pads)
Insul-Mat makes a line of fully inflatable ground pads that do not contain foam. This means that you need to inflate them orally. Their major advantages are that they are the lightest pads on the market and that they are fairly cheap. However, they do come with a price: if you aren't willing to sit in your tent and inflate your own pad after a long hike, then this kind of pad is not for you.

Hybrid Pads
Pads like Insul-Mat's Hyper-lite are a combination of a self-inflating foam pad, with a closed foam pad. Pads like this one gain the advantages (and disadvantages) of both open and closed foam.

Length
Except in the coldest conditions, you do not need a full body length sleeping pad. The additional comfort between a 2/3 and full body length sleeping pad is generally minimal. Most backpackers select a 2/3 length pad because they are lighter and they pack down smaller. Full length pads weigh more and therefore are popular for short hikes and / or car camping.

Thickness
Thicker pads (on average) provide more insulation, but weigh more.

Most sleeping pads' thickness lies between one and two inches, with under one inch thickness better for summer camping and over two inch thickness better for car camping (as well as rocky terrain).