I noticed today that Carbonite has updated its TOS (to conform to the EU-US Privacy Shield) and noticed also in the TOS under “conduct” that the terms do prohibit allowing illegal material to be backed up. “Illegal” could include delivery vehicles for malware, or copies of illegally downloaded content and possibly classified information or materials related to terrorism planning or c.p. It is probable that Apple and Microsoft and other backups (Mozy) have the same terms.
A few years ago there were a number of lawsuits against home users filed by media companies, mostly concerning materials downloaded and shared with others through P2P or possibly Bit-Torrent or maybe TOR. One of the most notorious cases was Sony BMG v. Tenebaum (wiki reference; law firm’s blog story). In a few cases (one in Minnesota) people were sued and judged against for what they claimed they had not done, but for what others in their households might have done.
It’s possible to get a warning of copyright infringement from an ISP. This would usually happen from P2P, but there are some articles about the possibility of a hack or misuse of a router from outside one’s home (such as this on “six strikes”). Most universities have policies on P2P (such as Washington).
Over time, the possibility could exist that the government could want to use automated tools, looking for digital footprints, to scan cloud backups. I doubt, however, that the various evolutions of the US Patriot Act and Freedom Act pose much of an issue for most users.