The answer your question exactly is yes. The only possible exception is cryptography in your country, if cURL was built with SSL support statically linked, or you're exporting from the US to one of a few countries considered hostile.
Scraping a site's publicly visible webpages is also legal, generally. If you download one copy each of all the pages you could see in your browser, you won't have any problems. If you start to cause problems for other uses, it might be considered a denial-of-service attack. You may also need to check with the site's terms or conditions, but since you already download it to view it, there isn't much difference (it's a subtle technicality, at best).
Downloading music, however, is just that. It doesn't matter if you use Limewire, uTorrent, Megaupload, Flashget or cURL, you're still downloading music. That's legal if the artist/record label says it is, if you own a license, or generally if you're legally allowed to do so.
So, cURL is completely legal. But like anything else, what you do with it may not be.