if you limit your panorama to a narrow vertical field of view, regular lens is ok.
if you want the sky(ceiling) and floor in the picture, fisheye is mandatory.
fishey also allow to take 2 or 3 pictures for a full view, while a dozen of picture will be needed wth a 24mm for example.
with my 8mm lens , i can do a full "bubble" , in only 2 pictures (while 3 are better).
the average of convering you need for a good stitching between 2 pictures, is about 30%.
so it means that only 30% of the field of view change between each picture (you need 30% at left and right).
This means a lot of picture to take. More picture means more work for stitching, plus the risk to have a bad exposed picture, or object moving between pictures that makes stiching more difficult.
Ideally , you have to rotate the camera at the nodal point, that is somewhere near inside the front of the lens. this prevent parallax of object (misalignement of close and far object in a different perspective.)
http://www.panoguide.com/howto/panoramas/parallax.jsp
For this, a standard tripod dos not fit, since the rotation is usually somewhere under the body of the camera.
There was a "cheap" accessory called NODAL Ninja
http://www.tawbaware.com/nodalninja_review.htm that help to mount the camera to have the nodal point of the lens aligned with rotation of the tripod.
you can do without it, but stitching will be less perfect.
idally when doing panorama, you will use bracketing (taking three shot at different exposure (-2, 0 +2 for example) so you can build HDR picture or panorama.
This is very nice because most of time, panoramic view includes some shot with sun or sunny window directly in the field of view.
The pope of panorama stitching is called Helmut Dersch and he developped some free tools to build panorama. You will find some graphical interface (GUI) using these tools as shareware like PTgui giving VERY professional results.
http://www.ptgui.com/