- Cropping - dead easy this one, simply take a single exposure as normal, and then crop it down to your desired format. Positives are that you can visualise how the final image will look, and your camera may even have guidelines in the viewfinder or on the LCD to help compose the picture. Also, this method works for moving subjects, can be used handheld and requires no additional equipment. Downside: you are throwing away perhaps half the resolution of your camera. Tip: to help with composition, stick a bit of semi-transparent gift tape across your LCD to show your preferred aspect ratio, but still allows you to compose using the full frame when you want to.
- Stitching - the basic principle is to create a row or rows of overlapping images that can then be 'stitched' together on a computer. Quite tricky to do without a specialist panoramic tripod head, which helps to eliminate parallax error so that the images captured will stitch accurately in your software (I use PTGui). Positives are you can achieve very high resolution images: typically when I create a 3:1 panorama using this method, the final image will be 40 to 80 megapixels, and that makes a high quality panoramic tripod head very economic compared to the cost of a higher-resolution camera. Of course, this method doesn't work with moving subjects, and can be quite slow and cumbersome to set up. It's also more tricky to visualise what the final image will look like. Oh, and that super-duper wide angle lens you just bought? Sorry, but you are more likely to be using a short telephoto with this method :-)
- Shift lens - both Canon and Nikon produce shift lenses that allow you to create 2:1 panos on full 35mm frame digital SLRs, and 3:1 on cropped-sensor cameras. You simply take 3 images, one shifted left, one with no shift, and one shifted right. These are then stitched in software as method 2. There is no problem with parallax as you are shifting the lens and not the camera, and it's slightly easier to visualise the results, especially using Liveview. However, shift lenses tend to be expensive and quite heavy.
For me, option 1 is really a stop-gap when an unexpected opportunity presents itself and there isn't time for the one of the other methods (or you don't have the right equipment with you!). My preference is for method 2, with 3 as an option when travelling light.