Maybe that's an area where online classes can innovate further: hard deadlines could be optional. People like me who want them could enable them when they start a course; people like you who don't, could disable them instead.
So there's no clear-cut answer. Making hard deadlines optional could very well cause more damage and less completion even if it's better for a few individuals. I hope that Coursera is collecting analytics on how people perform with different types of deadlines, so that they can come up with the best overall solution.
I just learned about the Neural Net class about a week ago and it's scheduled to end today. I decided not to let that stop me and went through all the lectures in a week. I'm going to have to watch a lot of them again, and I need some time to work with the concepts, but I enjoyed 'cramming' it all in one big gulp.
On the flip side, I stopped doing the Computational Finance at week 8 of 10, but I'll go back and finish it up over the holidays.
And on the third hand, the Modern American Poetry class I did was best done following the timeline, so that I go to participate in the forums at the same time as everyone else. That was a very forum heavy class, though, which is rare.
Anyway, I'm just glad all this stuff is out there now. I've learned a ridiculous amount in the last year.
In the case of edX, MIT's 6.00x course is strictly deadline based. CS50x allows you to take the course at your own pace as long as you finish everything before the 13th of April, 2013.
But those aren't the ones you're looking for. Udacity meets all your requirements. They have open enrollment, meaning you can join in at any time. Furthermore, they have no deadlines. As long as you complete all the problem sets and give the final exam, you get a certificate.
Here are some Udacity courses that might interest you:
Statistics 101 - http://www.udacity.com/overview/Course/st101 - Taught by Sebastian Thrun
CS271 Introduction to Artificial Intelligence - http://www.udacity.com/overview/Course/cs271 - Taught by Sebastian Thrun and Peter Norvig
CS373 Artificial Intelligence for Robotics - http://www.udacity.com/overview/Course/cs373 - Taught by Sebastian Thrun
Hope that helps.
Edit: There's CS188.1x by Berkeley on edX - https://www.edx.org/courses/BerkeleyX/CS188.1x/2012_Fall/abo...
It's deadline based, but I don't know whether they will remove their material at the end of the course or not.
Obviously, you can avoid this by downloading all the videos and slides as soon as you have access.
I believe that all Udacity courses are now self-paced. You can go through the lectures/quizzes/assignments whenever you want to.
Is it possible to review old courses and take them at my own pace, or are they completely gone once they are done?
Academic honesty is probably the biggest hurdle that online education is going to face. Once grades for these courses start to matter (and at some point, they will) there will be people in the world who will try to cheat.
to beat a dead conversation past the point of anyone caring other than me...
if you looked at the minute by minute activity, an honest effort to take a class should produce a fairly detectable minute by minute signature
for example, someone answering the questions who hasn't watched the whole video, unlikely to be an honest effort
there are enough data points in there, that detecting cheating should really be a question of mining the right data points
For all of the courses I've taken (ML, PGM, NLP, SNA) I've followed roughly the same pattern: follow the course for 50-70% of the material doing all homeworks etc. Take what I've learned and go off do some fun projects. Once I hit a road block return to the course and finish up (usually months after the course is 'officially' done) typically forgoing the homework being I've already created 'homework' for myself.
Compared to my classroom experiences, I've found that this method greatly enhances the benefit of the materials I learn later in the course, as well as allowing me to more strongly reinforce material learned earlier. This is also something that physical classes simply cannot emulate. I do find it a little funny that I've never officially completed a coursera course, despite having covered much of the material very thoroughly. Hopefully as these courses continue we'll start to see them adopt patterns that extend beyond replicating the limitations of a physical classroom online.