If you're running a RH based distro and want to install a .DEB file, you could also try using 'alien' (or something like that). Since the ideas behind both file-types are the same, and the processes to create them are more than likely to be, at the very least, similar, there is no real reason that packages from one should not work on another.
However, not all distros use exactly the same directory structure. Therefore should you install a package from a distro with a different dir. structure to yours, although the files will have been installed, your distro might not be able to run it (i.e. it doesn't known where the files are).
The 'Package Manager' program that comes with Mandrake (by the way, it is not the one that starts by default under Konqueror, you will probably have to go K>Configuration>Packages>Package-Manager assuming you're using KDE) will allow you to check the dependencies (i.e. you might need some files (what Windows would probably call .DLL files) installed before you can run the program) of a given package. Also, in the right-hand pane of Package Manager, there should be a 'tab' that shows you the files to be installed, and the directories into which it wants to install them.
I haven't ever used a Debian distro (yet - I've just bought a magazine with Progeny on it's cover DVD) so I'm affraid I can't really help you there.