The Waterloo BragZone (http://links.uwaterloo.ca/bragzone.base.html
or ftp://links.uwaterloo.ca:/pub/BragZone/ ) compares the results of
various image compression schemes against a 32 element test suite.
Sample images are available.
The Computer Vision Home Page has many links to test images in
http://www.cs.cmu.edu:80/afs/cs/project/cil/ftp/html/v-images.html
A bunch of standard images (lenna, baboon, cameraman, crowd, moon
etc..) used to be in ftp://eedsp.gatech.edu/database/ . The
images are in 256-level grayshades (256x256 pixels, 256 "colors").
[Note: the site ipl.rpi.edu mentioned below keeps changing. Images
stay there for a while then disappear. They are again available at
the time of writing (27 Dec 93).]
The site ipl.rpi.edu (128.113.14.50) has standard images in two
directories:
 ftp://ipl.rpi.edu/pub/image/still/usc 
 ftp://ipl.rpi.edu/pub/image/still/canon
(The directory /pub/image/sequence was taken offline because of
possible copyright problems, but has come back again. In particular,
Miss America is in subdirectories of /pub/image/sequence/missa.)
In each of those directories are (usually) the following directories:
 bgr - 24 bit blue, green, red
 color - 24 bit red, green, blue
 gray - 8 bit grayscale uniform weighted
 gray601 - 8 bit grayscale CCIR-601 weighted
And in these directories are the actual images. 
For example, the popular lena image is in
 ftp://ipl.rpi.edu/pub/image/still/usc/bgr/lena # 24 bit BGR
 ftp://ipl.rpi.edu/pub/image/still/usc/gray/lena-y.ras # 8 bit gray
All of the images are in Sun rasterfile format. You can use the pbm
utilities to convert them to whatever format is most convenient.
[pbm is available in ftp://ftp.ee.lbl.gov/pbmplus*.tar.Z ].
Questions about the ipl archive should be sent to help@ipl.rpi.edu.
There are few gray-scale still images and some raw data of test results
available in directory ftp://nic.funet.fi/pub/graphics/misc/test-images/
There are lots of .gif images in ftp://nic.funet.fi/pub/pics/
Medical images can be found in:
 ftp://decaf.stanford.edu/pub/images/medical/
 ftp://eedsp.gatech.edu/database/images/wchung/medical
 ftp://omicron.cs.unc.edu/pub/projects/softlab/
The WWW address for the National Library of Medicine is http://www.nlm.nih.gov
A list of health and medical related Internet resources is available ftp://in
ftp.sura.net/pub/nic/HealthResources/medical.resources.3-94
Rodney Peck <rodney@balltown.cma.com> is interested in some method
of establishing a canonical ftp database of images but does not have
the resources to provide an ftp site for that database. Send suggestions to
rodney@balltown.cma.com.
Beware: the same image often comes in many different forms, at
different resolutions, etc... The original lenna image is 512 wide,
512 high, 8 bits per pel, red, green and blue fields. Gray-scale
versions of Lenna have been obtained in two different ways from the
original:
 (1) Using the green field as a gray-scale image, and
 (2) Doing an RGB->YUV transformation and saving the Y component.
Method (1) makes it easier to compare different people's results since
everyone's version should be the same using that method. Method (2)
produces a more correct image.
For the curious: 'lena' or 'lenna' is a digitized Playboy centerfold, from
November 1972. (Lenna is the spelling in Playboy, Lena is the Swedish spelling
of the name.) Lena Soderberg (ne Sjooblom) was last reported living in her
native Sweden, happily married with three kids and a job with the state liquor
monopoly. In 1988, she was interviewed by some Swedish computer related
publication, and she was pleasantly amused by what had happened to her
picture. That was the first she knew of the use of that picture in the
computer business. A scan of the original Lenna from Playboy is available at
http://www.cs.cmu.edu/~chuck/lennapg/lenna.shtml
The editorial in the January 1992 issue of Optical Engineering (v. 31 no. 1)
details how Playboy has finally caught on to the fact that their copyright on
Lena Sjooblom's photo is being widely infringed. However Wired says in
http://www.wired.com/news/culture/story/4000.html "Although Playboy is
notorious for cracking down on illegal uses of its images, it has decided to
overlook the widespread distribution of this particular centerfold".
The CCITT (ITU-T) test images are in ftp://ftp.cs.waikato.ac.nz/pub/ccitt/
and http://www.cs.waikato.ac.nz/~singlis/ccitt.html
[The images in ftp://nic.funet.fi/pub/graphics/misc/test-images/ccitt*.tif are
corrupted.] This set is commonly used to compare binary image compression
techniques. The images are 1728x2376 pixels.