Solution 1:

You can try: http://www.uccs.edu/math/student-resources/video-course-archive.html

They have a Real Analysis course listed, Math 533 Real Analysis I - Fall 2007. They are good, though not that challenging.

You may need to create a [free] account to view the videos.

If you really don't want to make an account the videos start with:

http://cmes.uccs.edu/Fall2007/Math533/pages/video3.html

and go up to /video24.html. There is, for some reason, no video 1 or 2.

Solution 2:

Video Lectures in Mathematics , This site contains links to math videos, withch includes a lot of mathematical topics for example Topology, Algebra, Complex and real analysis and anything that you think.

Specifically, the site has 38 videos in real analysis: Analysis, Real.

Solution 3:

Check out these YouTube video lectures by S K Ray on real analysis.

Solution 4:

This was basically already posted by Alex - but Joel Feistein has his 2nd year undergrad introductory course to real analysis (complete with camcasts/videos, notes, exercises and solutions) posted here http://unow.nottingham.ac.uk/resources/resource.aspx?hid=c6c045f6-286d-6b9f-b96c-36a998632fc3 and his 4th year undergrad course on functional analysis here http://unow.nottingham.ac.uk/resources/resource.aspx?hid=c9eec1dc-8c27-9949-dc16-2728edf6c994.

They are both quite good (the first one introduced me, at the time an engineering undergrad, to rigorous mathematics and how to do proofs and I cannot be happier of having watched it).

Solution 5:

In fact I ended up using Nottingham Uni's lectures on Youtube, like this one:

http://www.youtube.com/watch?v=mB4Yny0T3HA