You don't always have to have a tripod with a panorama head to shoot good panoramas. With today's stitching software all you need to do is follow some simple basics to get good usable panoramas straight from the camaera with no tripod.

Step 1: The Parallax Problem

The main reason for using specialized equipment such as a tripo fitted with a panoramic head is to eliminate parallax. So before describing how to shoot panoramas handheld, I think its best to give a brief (non technical) description of Parallax the main culprit for panorama failures. Parallax is the affect that you can see when you hold your finger in front of your eyes and look through it at a distant object, then alternately close one eye and then the other. Your finger moves in relation to the background. what is really happening is that your eyes are looking at the scene from a different viewpoint and introducing Parallax. The same thing happens if we take a photograph of an a foreground object that is in front of something else in the distance (say a car nearby parked in front of a building in the distance). If we took one photo then took a step to the right and took a second image, we would see that the car is in front of a different part of the building. This is bad for shooting panoramas as we need to stitch multiple adjacent photos together to make the entire image. If each photo is different due to parallax then the stitching software will have a hard time.

In the diagram above the addition of parallax will make to adjacent images in a round of panoramas different from each other. This is particularly true when there is an object in the foreground that interacts with a background object. With a lot of parallax you may end up with stitching issues.

Step 2: Minimizing Parallax

To minimize the impact of this we want to reduce Parallax as much as possible. Ideally you can use a tripod fitted with a Panorama head. this will rotate the camera about the no parallax point and as the name suggests result in a round of shots in the Panorama that should not have any noticeable parallax issues. If a panorama head is not available then mounting the camera to a normal tripod will introduce some consistent parallax. For handholding the technique of turning is very important as our natural tendency is to rotate around our feet. this will cause some significant parallax issues. One way to overcome this would be to make an effort to rotate around the camera and in fact rotate our feet in a small circle. As shown in the diagram above

Step 3: Handheld Friendly Panoramas

In addition to trying to minimize Parallax you can select your subject to make your life easier, as not all scenes will be handheld friendly. Parallax becomes an issue if there are complex interactions between objects that are close to the camera and objects that are further away. If a scene has little variation in how far the objects are from you, or there are very few foreground objects interacting with your background then the parallax issue will be minimized.
This doesn't mean to say the image has to be boring as Stone Henge would make a great handheld pano friendly subject.

So try to avoid scenes with a high degree of foreground objects that interact with the background objects. If you do have some key foreground interactions try to shoot them dead central to the photograph so they are not the main stitching areas.

Step 4: Camera Setup

To make a good panorama, handhel or not you want the settings to remain constand through all of the exposures, that means everything will need to be set to manual. In order to set a good exposure the following steps can be used

Set to Aperture priority and set the aperture to give good depth of field say 9.0

Take four readings at 90 degrees apart to get the min and max readings.

Average the readings and switch to manual mode, dial in the aperture and shutter speed based on the average.

At this point check the shutter speed isn't too low for handholding, if it is either increase the ISO or increase the aperture size.

Take some test images to see that the detail that you're interested in is coming out (i.e. if the sky is important make sure you're not blowing it out and if some of the darker areas are important make sure they're not underexposed)

Focus on the main subject area of your image and switch to manual focus

Set the white balance to one of the manual modes.

Now you're ready to shoot the scene

Step 5: Shooting the Scene

When shooting on a tripod with a panoramic head, you can easily calculate how many images you need to make up the scene. however when handholding I wouldn't bother trying to stick with a set number of shots. It is much better just to focus on maintaining a good overlap from shot to shot, and trying to move around the camera (and not your feet)

Start with the first frame and line up the focusing points with key features of the scene. Scan your eye to the right hand side of the screen and make a note of what features align with the right hand focusing point.
Take the photograph then moving your feet to rotate as much around the camera lens as possible, line up the features of the scene that were on the right of the viewfinder with the focusing points on the left of the scene.
Complete the round of photographs until the whole scene has been captured.
Repeat rounds of panoramas tilted up and tilted down.

The picture shows how you can use features of the scene to line things up as best as possible.
As you can see from the example in the picture I have decided to make life easier by investing in a grid type focusing screen. in stead of the standard focusing points it also shows a grid of horizontal and vertical lines whcih can be used to facilitate the lining up of frames.

Step 6: Stitching the Images Together

Once you've had a bit of practice shooting handpanoramas you'll find when you stitch your images together you'll get a bigger and better final image.
I use photoshop photomerge to stitch all the photos together, but there are many other software packages that can be used.
Using photoshop select File > Automate > Photomerge
to bring up the photomerge dialog box.

Select all your handheld files and process them, I always try using the auto setings first and if that doesn't work try the perspenctive and spherical options.

Step 7: What to Do With Your Panoramas

Once you've created your hand held panoramas, you can leave them as panoramas, or try to do something else with them.
I use my panoramas to create PanoPlanets by rolling them into little planets.

For more examples and in depth tutorials check out my website dedicated to PanoPlanets at
http://www.panoplanets.com