As JayC30 mentioned, the UK seems to be one of the few countries where the authorities or music labels plan on suing those who purchase music from illegal sources (which they consider). However, I'm not aware of any news where consumers were sued for buying music online, at least where uploading is not involved. In fact, if the music labels do start doing this, I would not be surprised of consumers start backing off from all online stores altogether if they have no clear means of checking whether they are legitimate. For example, if you were to ask someone who never heard of Allofmp3 or iTunes and to examine both sites and mention which is considered legal or not, there is no clear indication until they start researching elsewhere.
In the US, the main people the RIAA are after are those who share music. They say they are going after downloader's, but the users they actually go after are those sharing out over a certain number of tracks (usually around a 1,000 up). Their main interest is to make it clear that copyrighted music is not 'free'.
If the RIAA or any other music label decided to start targetting downloader's specifically regardless of whether they upload, they are not going to get very far apart from a short term slowdown as what happened when the RIAA first started suing P2P users. In fact, they seem more interested in trying to shut down what they consider the illegal online stores such as AllofMP3 rather than try targetting the store's customers, particularly since consumers feel like they are doing the right when they decide to start buying music instead of freely downloading it.