I am always interested in seeing what people have to say about the practicalities of shooting panoramics. This discussion seems to have fallen into a more purist, technique centric view (panopeeper and friends) and a more free-form dynamic method.
Both Work Well!!!
I use both handheld methods, and tripod mounted with a spherical head setup. I have gotten excellent results with both, but here are few observations from my field experience:
1) Handheld frequently drifts from level and ends up requiring more aggressive cropping than you might hope, as panopeeper demonstrated
2) Double-row using handheld methods is difficult to do with high-quality particularly with more than about 2x4 images
3) Well-done foreground in a panoramic makes a fantastic element of composition, so careful calibration is very useful
4) Using a tripod doesn't eliminate mistakes http://www.trailpixie.net/panoramics_go_b.htm
5) Panoramic images that project well below or well above the horizon demand a spherical head setup to get reliable results.
I have never worked with tilt-shift lenses, though I have considered it. Related to this topic, one thing that hasn't been discussed is the focal length of the lens you choose for panoramic images. If you plan to do substantial corrections for parallel straight lines, in building perhaps, a longer lens allows you to take more images resulting in a higher resolution and less impact from the dreaded pixel-stretching.
I haven't met very many people who routinely shoot panoramics at 70mm, 100mm, or even 400mm. There are some pretty cool perspectives that can be achieved with these longer lenses, and the stretching and warping that you may end up doing doesn't have as deleterious an effect as it would if you shot fewer frames at a wide angle.
So, proper spherical tripod head technique, with longer focal lengths substantially reduces the necessity of tilt shift lenses, as long as you are willing to deal with the reduced spontaneity.
As for working quickly and spontaneously, I don't find that panoramic photography is highly compatible with that kind of work (though I have experienced notable exceptions http://www.trailpixie.net/general/sand_water_sky.htm
). this doesn't diminish it power as a creative technique. I see a great image and I know it can't be captured by a wide angle lens because the resolution won't be high enough. I shoot the image in panoramic form and then get back to my computer and am excited to see the image take form--I am only pleased when the image is printed 24"x48" on my viewing table. That is when the composition is realized. Like old-times, eh.