Some of the things that I have seen white-papers be useful for:
Position papers, manifestos, and other intellectual opinion statements.
Disseminating protocols, techniques, standards proposals, and other things that are useful but "below the threshold" of a normal publication
Seeding discussions with program managers and other potential funders and collaborators.
Date-stamping a piece of work so you can get it out of your queue and move on. Much better a white paper in an informal repository than a disreputable journal.
Sometimes white papers end up "upgrading" into proposals or publications of various types---sometimes very high impact publications. Sometimes they even draw a surprising amount of citations. Mostly, though, they are for the less formal side of scientific life. A well-regarded white paper sort of statement can change the course of an entire field.
One thing that I think is very important is, for any white paper that you are disseminating publicly, to get it into some archival location. There are a number of methods for this, from arXiv to standards RFCs to institutional technical report collections. If do this, it will be much easier for people to cite your white paper, pass it around, and generally disseminate it. And if it's persistent, you can feel much more comfortable adding it you your C.V...