In reply to Matt Milton:

I think it may depend on where you download it from, but in many cases you simply have a licence to use downloaded material, rather than owning it, and that licence can be revoked if you breach their conditions. I recall a case where a woman had her Kindle wiped by Amazon because she'd downloaded ebooks from a different location to where she was licenced for and was in breach of their copyright agreement. The licence may be linked to your iTunes or Amazon account and may not be transferable - Bruce Willis was reported to be suing iTunes so he can pass on his record collection to his children.

Do you own your record collection?

I think if you purchase a download direct from the artist you are probably OK. I think Bandcamp may be OK as well - they reserve the right to remove downloaed material for copyright reasons (eg it turns out the artist didn't own the rights) but they recommend you copy it to your own device so it is safe from them.