Also the Germans are going nuts about it because they claim the Origin EULA is a violation of privacy laws:
http://www.gameranx.com/updates/id/3477/article/origin-s-inv...
I was under the impression that Steam's anti-cheat bot actually did something similar to this too, scanning running programs to search for aimbots and the like. This might go further though, I have no idea if it scans non-steam folders.
There's a provision in german law that EULAs may not contain clauses deemed "surprising" or "unexpected". There are multiple paragraphs in the Origin EULA that violate this principle (such as reserving the right to scan all data on your computer).
There's another rule that customers may not be placed at a significant disadvantage if you're dealing with private customers. This rule is violated for example when EA reserves the right to terminate support for the game (rendering it effectively unusable) at any time at their sole discretion.
There's other minor points such as attempting to move eventual lawsuits out of country or reserving the right to unilaterally change the EULA at any time but that's more or less the icing on the cake.
The obvious consensus is that the EULA is invalid in pretty much any given point. Which means that the game is defective and may be returned to the store at any point after buying - a tempting idea actually :)
In other news: EA seems to back off a little http://www.heise.de/newsticker/meldung/Electronic-Arts-reagi... (german as well)
They removed it from the Origin Terms of Service, which is nice, but left it in the privacy policy, so the overall change is... nothing.