Tripods make your pano shooting experience much, much easier than if shooting by hand.
All the reasons why one would use a tripod to shoot any photo, apply to pano shooting and more.
So why do you want to use it?
Let me quote two very famous photographers instead:
John Shaw, author of "The Nature Photographer's Complete Guide to Professional Field Techniques".
If you want to improve the quality of your photographs the best single accessory you can buy is a sturdy, well-made tripod. Every working professional nature photographer shoots every exposure possible with his or her camera mounted on a tripod.
John Fielder author of "Photographing the Landscape: The Art of Seeing", writes:
You can make good photographs while hand-holding the camera, but you won't achieve excellence. A tripod and cable release of the shutter are as important to the landscape photographer as the shovel is to a ditch digger.
Reason 1: Tripods allow you to have a rock steady shooting platform.
The best panos always have great depth of field. Without getting into the technicalities of it, depth of field refers to the fact that close objects as well as far objects are in focus.
If you don't have much light then the camera will make some compromises by slowing the shutter speed so much that it will be exremely hard for you to hold the camera absolutely steady while having an apperture that gets you depth of field.
With a tripod it doesn't matter since its job is to hold the camera steady.
Advantage, tripod.
Reason 2: Tripods allow you to have the pano shooting sequence absolutely level.
In a previous entry I mentioned a gadget that when attached to the flash hot shoe of the camera, would tell you if the camera was level or not. A pano sequence, to be able to produce a great pano image, has to be shot absolutely level. If it is not, then the software will have to work that much harder to align images that by nature are not aligned causing the final results to be less than ideal.
It causes the software to assemble the images in a "staircase" faction. This ultimately causes the images to have to be cropped much more dramatically leaving precious pixels out.
Advantage, tripod.
If you are curious which tripod I use, I have two. An old, very heavy but very solid one, primarily intended for video, that was made by Slik. The model sticker fell off years ago...I don't know the model :-)
I never take it with me on the field.
The other one is a Bogen - Manfrotto 055XB tripod with a Bogen-Manfrotto 488RC4 Midi Ball Head using the RC4 Rapid Connect System.
Tripod

Head
Coming up: what made me decide on this combination.
Those are made of carbon fiber or the new "in vogue" material: basalt fibers.
Unfortunately they are expensive. Very expensive.
A top of the line Gitzo basalt tripod with matching head, can cost you many hundreds of dollars.
The perfect tripod is: lightweight, built like a tank and costs little. Unfortunately you can have only 2 out of 3... but never all three.
Take a look at Thom Hogan's site. He is one of the luminaries in this field.
His "walkaround" tripod legs (Gitzo GT2540) goes for almost $600 at adorama.com.
And this is without the head...
Ouch!