/System/Library/Frameworks/ApplicationServices.framework/Versions/A/\
Frameworks/LaunchServices.framework/Versions/A/Support/lsregister -dump
You should be able to copy and paste that, thanks to the backslash. But if you can't, just make it one long line with no added spaces. This command will list all LaunchServices information. The output will look something like this:
B00001572 APPL/ddsk Thu Aug 5 21:25:59 2004 DiskImageMounter.app
-pad----hn---s--A---- v76.4.0 DiskImageMounter
Contents/Resources/diskcopy.icns com.apple.DiskImageMounter
Contents/MacOS/DiskImageMounter 12556, 1728655, Mach-O
V00000008 /System/Library/CoreServices/DiskImageMounter.app
C00001344 NDIF disk image
viewer, default, apple, Contents/Resources/diskcopy-doc.icns
.ndif, 'dimg', 'hdro', 'rohd', 'hdcm'
C00001351 NDIF disk image segment
none, default, apple, Contents/Resources/diskcopy-doc.icns
.imgpart, 'dseg'
....
The B entries list the programs' basic info (in this case, for DiskImageMounter.app). The C entries below that show which file types the program will accept, with both a description and a list of extensions. So there you have it; everything your machine know about. But the question is ... how do you clean out all the applications registered on unmounted DMG volumes which show at the end of the list?
[robg adds: To me, at least, it seems this hint is mostly in the "hmm, that's interesting" category, as I can't see any way to directly modify or change the info it holds (not that you would want to do so under any normal circumstances!). So give it a whirl if you'd like to see every app that your system knows about; you might want to put | more (or | less) at the end of the command to control the paging.]

