According to messages on the official Mass Effect forum, both Mass Effect and Spore will use the SecuROM online activation. This is the way that Bioware has chosen to fight piracy.
Unfortunately, the same thing happened with Bioshock, and if you somehow managed to miss it, you can check it out here and here. Bioshock became known for its protection issues. Derek French, Technical Producer, has also noted that Mass Effect will use SecuROM and after the first activation it will need to re-check with the server every ten days.
The bottom line is that this might upset Internet-less gamers, and if things get bad, as they did with Bioshock, even those gamers that decided to buy the game. Piracy is a big problem, but this game will also be cracked eventually, so why all the hassle?
You can find the original thread here.