I'm running InDesign CS 3.0.1 on Mac OSX 10.4.4. My printer is a Canon
 PIXMA ip3000. When I attempt to print out a document from InDesign,
what should be pure black comes out medium-dark  gray. It isn't the
printer that's at fault, because this doesn't  happen with other
programs. Furthermore, if I save the same InDesign document as a PDF,
and print it out from a PDF editing/viewing  program, the blacks are
correct!!

In order to try to solve this  problem myself, 

+ I've checked to make sure there is no tint  adjustment less than 100%. 

+ I've tried printing in  "registration" and in "black" to see if
there was any difference  there. There wasn't.

+ I also went through the print settings. The  only one that seems to
affect ink color is "Output". It offers two  selections: "Text as
black" and "Simulate overprint." It makes no difference if either of
these are checked or left unchecked.

+ I deleted the SavedData file and the Defaults file. 

+ Finally, I reinstalled InDesign 3.0 on a separate hard drive,
updated it to 3.0.1 (which maybe wasn?t so smart), and printed the
same pages. Same gray.

Finally, I should note that I think this problem emerged in the last 
month or so, but I can't remember when or what I might have done to
make it happen.

I'm having basically the same problem. Indesign CS2 4.0.2 on a PC.
Wherever I place an image (psd) with a transparent background on an
area designated with a black background in a layout, the black prints
out darker than the background within the transparent area of the
image. Other colours do seem fine though and do not simulate this
"overprinting" problem.