Ideally the tool should be
- easy to use
- able to work with images taken without a tripod (i.e. allow to align the images)
First and foremost, the best "tool" for creating HDR images is having a proper understanding of what HDR is, and why you might need to use it. Most people are familiar with the classic "HDR Look", while at the same time not fully understanding why the classic HDR look is not necessarily how an HDR image should look.
HDR, or high dynamic range, is a means of increasing the usable, functional range of contrast and color depth in a photo. Realistically, this provides greater flexibility when working with such an image, but there should not be any fundamental differences in how the resulting image looks.
My preferred tool for working with HDR images is Photoshop. Adobe Photoshop, for several versions now, has offered a
Merge to HDR tool. This tool allows you to select multiple shots of differing exposures to merge into a single 32bit, high dynamic range image. The merging process will automatically align your images and attempt to remove undesirable artifacts. (Note: Photoshop CS5 improved the HDR features, and added a deghosting capability that helps when merging hand-held shots.) Once created, you have the option of applying a tone map to the image when downconverting to 16 or 8 bit, which allows you to pick the range of tones you wish to utilize, and map them to the target color space. The final result should look like a normal photograph, just with a greater range of tones that extend beyond what you would normally be able to achieve with a single shot with the normal 5-7 stops of most digital sensor, or 5-9 stops of film or high-end digital sensors.
Another popular tool is Photomatix. This tool is explicitly designed to generate HDR images, and it has a fairly rich feature set. Photomatix is well known for creating images with that "classic HDR look", and if that is what your looking for, this is definitely the tool you want. There are some drawbacks to Photomatix, however. It sometimes has problems with generating noise, rather than eliminating it, when merging multiple shots. The end result is grainy images that have larger grains than your normal digital noise, but on par with film grain. Another quirk of Photomatix is that sometimes it caps off highlights lower than it should, limiting the available dynamic range you have to work with for bright highlights.
Hugin will meet needs 2 and 3. Not sure about #1, but try it out and see if it's close enough.
Try Luminance HDR. It's free (open source).
UPDATE 26/12/2016: Moved to github for source
This flickr group can also show you some examples of HDR being used.
If you are not afraid of using the command line interface, then I can recommend align_image_stack and enfuse. I like the default settings. The output is not the cartoon like image. Details appear on the bright and dark areas.
The simple commands I use
align_image_stack -a prefix input1.tif input2.tif input3.tif
It generates prefix0001.tif prefix0002.tif prefix0003.tif. The next step is enfuse
enfuse -o HDR.tif prefix*.tif
Photomatix and Photoshop are the big ones, Hugin is the free option but nobody mentioned oloneo - www.oloneo.com . I personally like Oloneo next to my Photoshop CS4 - the advantage I see in Oloneo over Photomatix are significantly simpler controls.
While not free, if you're on the Mac, I really like Aurora HDR from MacPhun. Its default settings tend to be a little much, but once you dial them back, it's quite a useful tool for getting good results.
Hugin as mentioned in the other answers, but only to align the images, and then ImageJ to produce the HDR image using tonemapping that you can then easily program yourself.