It's worth noting that some classes do actually disable access to the lectures and course site for students after a cut-off date. I can't speak for all of the classes from these schools, but all the classes I've taken from Princeton, Johns Hopkins and U-Penn through Coursera do that.

They do allow you to download the videos, so if you're planning on taking a class from one of those schools at your own pace, just be sure to download the lecture videos and slides before the end date.