I really loathe the idea of internet checking. It makes everything a lot easier for hackers, spy/adware and viruses to get at your system.
Don't forget, all the time you are playing your game you will be online - with no idea of what is happening behind the game screen. In that time, you are absolutely vulnerable to hackers.
Sure, copy protection can be a pain - but at least it isn't an open invitation to anyone who wants a shot at your system.
The other thing is - what happens if a company goes bust? Its server goes offline, and every single one of the games you have by that company are completely unusable forever thereafter because the internet checking system will be unable to connect to anything.
It also won't make games more forward compatible than copy protection, because the main problems are usually more to do with advances in DirectX or Video/Sound Cards making old games obsolete because they are trying to use features that no longer exist because they are so outmoded.
All in all, I consider internet checking to be a system with many drawbacks and no positives whatsoever. Like Plowking, I won't touch any game that has it.