I use MacPorts on Mac OS X, which is a source based package manager; each Portfile contains a description of how to download, patch, compile, and install a piece of software on Mac OS X. Included in the Portfile is the checksum of the particular version of the tarball to download. This helps ensure the integrity of the file from many possible problems; sometimes, people will update a tarball without incrementing the version number, which may cause patches to fail to apply or the code to break under certain conditions, or sometime the package may become corrupted, or an attacker may be tampering with the software in the hopes that you will install it.
So, I will have to say that yes, I use the checksums every time I install software (though my package manager does it automatically for me, I don't do it directly). And even if you are downloading manually from a respectable project, you many wish to download the code itself from a faster, closer mirror, and then verify the checksum against a copy downloaded from the more trusted master server; that helps keep it more difficult to attack as multiple servers would have to be compromised rather than just one mirror.