* A generic provider of CPU/storage/bandwidth who isn't (generally speaking) responsible for users copying stuff using provider's resources.
* A service who clearly and obviously caters to pirates (those do actually get in legal trouble)
A lawsuit would probably be interesting for the class of cases where it is not clear who is legally responsible for actions performed by software (author, owner of box, user starting the action, etc.)
" (a) Transitory Digital Network Communications. - A service provider shall not be liable for monetary relief, or, except as provided in subsection (j), for injunctive or other equitable relief, for infringement of copyright by reason of the provider's transmitting, routing, or providing connections for, material through a system or network controlled or operated by or for the service provider, or by reason of the intermediate and transient storage of that material in the course of such transmitting, routing, or providing connections, if - (1) the transmission of the material was initiated by or at the direction of a person other than the service provider; "
To make that claim, they need to register a designated agent first; I can't find their agent on their online listings or their website, but I presume that they will do that before they get too big.
Disclaimer: IANAL, this is not legal advice.