I'd be very careful with requiring an internet connection to use your product. If you must please at-least for the love of god make sure you handle less common connection types such as authenticated proxy servers (ideally depending on the OS you should be pulling all the network settings from the OS wide settings), I've seen so many developers that add in online activation support that don't take into account that not all internet connections are the same as theirs and don't allow how the app connects to be customised.
(A little background for the curious - I work in a company that works with sensitive data and we have strong security requirements that include the only Internet access being via a authenticated proxy server. I've spent many a frustrated hour dealing the apps that require online activation but won't connect to their servers using the only connection type we are allowed to go out via (not my decision, it's mandated by clients and upper management many levels above my head), doesn't matter how awesome said app is if we can't get the drm to work we will be buying your competitor's product instead. One time activation atleast can be done by connecting a machine to a non secure network for a minute but if ongoing access is required we have no way to make use of the app...)
As a software developer myself I understand concerns about limiting piracy (I often ponder the questions in this thread myself when thinking about potentially writing a commercial game in the future) but I think expecting it to phone home regularly is risking making it unusable for a subset of potential customers and might just hurt you more than it helps? (Depends just how many people will be stuck unable to use such drm, I don't have info on just how many networks are as locked down as the one I'm on so I can't really say).
Only other thing I can say is that I've bought every single humble bundle (and paid well over the average price) barring one I missed but I make a point of never buying anything that has heavy drm in it (no I don't pirate it, I just don't use software that requires heavy drm to run).