Although I might be preaching for the choir... Please note that the majority of "streaming" services in the internets are not streaming anything. They are mostly flash applets that download the file in it's entirety into your browser cache and play it from there.
It is retardedly simple to open the cache in file manager and copy-paste-rename the appropriate files if one wants to, and the only thing preventing you from doing it might be willingness to abide by the license agreement of the service in question (which likely forbids you to make local copies; however I personally don't see much of a difference between a file in cache and file somewhere else so it's something of a line drawn in water anyway).
Real streaming is somewhat different, and used for different purposes. Like internet radio channels. Or podcasts. Or NASA TV. Real streaming always requires the transfer rate to be at least the same as the bit rate in the media; this is not the case in, say, YouTube or other video sites. If you have slower connection, you can just pause it and it downloads the video, letting you to watch it later when it's downloaded entirely into local cache.
Not that real time streams aren't really easy to copy for future use as well, but that's neither here nor there.
Legally, I don't think it's any more acceptable to put up songs or stuff for streaming than it is to put them up as direct downloads, but technological ignorance from behalf of both users and rights holders has so far prevented this from becoming much of an issue. Although some rights holders do seem to be on a YouCrusade to get their stuff out of Tubes.