What are the best online, college-level mathematics courses?

There is something which very few people know about. The Abdus Salam International Centre for Theoretical Physics at Trieste, Italy has a one year Diploma programme with courses which are somewhere in between the undergraduate and graduate curriculum in most US universities. The good thing is that, the lectures of many years are available online here: EyA Recordings of the ICTP Postgraduate Diploma Programme and the quality of recordings and voice is not bad. Some courses like Dynamical Systems, Differential Geometry, PDEs are really very good and must be given a shot it.
Additionally, MIT OCW has a huge collection of undergraduate and graduate level courses in mathematics (and other subjects as well) which includes audio/video lectures, lecture notes, textbooks, assignments, exams and other interactive stuff etc.

Besides that there are a bunch of other online resources listed below:

• Ted Chinburg's Lectures on Algebraic Number Theory

1. Tables of current homework and lecture schedules
2. Tables of current homework and lecture schedules
3. Tables of current homework and lecture schedules

• Lectures by Adrian Banner of Princeton University

1. Calculus I : Calculus I (Princeton University)
2. Calculus II : Calculus II (Princeton University)
3. Calculus III : Multivariable Calculus : Calculus III: Multivariable Calculus (Princeton University)
4. Linear Algebra : Linear Algebra (Princeton University)

• Eugenia Cheng and Simon Willerton of the University of Sheffield, a.k.a. The Catsters' Video Lectures on Category Theory : TheCatsters

• Abstract Algebra lectures by Prof. Benedict Gross, Harvard : Abstract Algebra

• Lectures on Complex Analysis by Tibra Ali (followed by few more lectures on different topics) : Perimeter Institute Recorded Seminar Archive

• Lectures on Complex Analysis by Prof. P. A. S. Sree Krishna : New User Registration

• Lectures by Denis Dalidovich on Variational Calculus and Gaussian Integrals (followed by few more lectures on different topics) : Perimeter Institute Recorded Seminar Archive
• Geometric Representation Theory by John Baez and James Dolan :Geometric Representation Theory Seminar: Fall 2007
• Miles Reid's lectures on Algebraic Geometry and Algebraic Surfaces

1. VOD the MathNet Korea
2. VOD the MathNet Korea

• Videos from Summer School of Clay Mathematics Institute on Arithmetic Geometry (You should have a solid foundation of algebraic geometry in order to comprehend these videos) : Clay Mathematics Institute Summer School 2006 Recorded Lessons

• A mini course on Additive Combinatorics taught at IAS by Boaz Barak, Luca Trevisan, and Avi Wigderson : Page on princeton.edu

• Lectures on Real Analysis by Prof. S.H. Kulkarni, Department of Mathematics, IIT Madras : New User Registration

• Point Set Topology videos :

1. Topology - YouTube
2. General Topology

• Sets, Counting, and Probability by Paul G. Bamberg, Harvard University :Sets, Counting, and Probability

• The Fourier Transform and Its Applications, taught by Brad Osgood at Stanford : Stanford School of Engineering

• Courses by Stephen Boyd at Stanford:

1. Introduction to Linear Dynamical Systems - Stanford School of Engineering
2. Convex Optimization I - Stanford School of Engineering
3. Convex Optimization II - Stanford School of Engineering

• Prof. Gilbert Strang's course on Linear Algebra at MIT : Linear Algebra

• Differential Equations, taught by Arthur Mattuck at MIT : MIT 18.03 Differential Equations - Spring 2006

• Video lectures for elementary differential equations with linear algebra :Differential Equations Videos

• This URL provides video lectures on key concepts of calculus : Calculus Videos

• This URL contains a series of video lectures on Calculus I from University of Missouri - Kansas City : Course - Calculus I with Professor Richard Delaware

• College Algebra taught by Professor Richard Delaware, which consists of 40 video lectures emphasizing the concepts of college algebra : Math 110: College Algebra

• More lectures on Real Analysis by Professor Francis Su Harvey, Mudd College (The video quality of the lectures are poor) :
  

• MIT OCW - Calculus Revisited: Multivariable Calculus. This course is a study of the calculus of functions of several variables (vector arithmetic and vector calculus) : Calculus Revisited: Multivariable Calculus

• Very quick graduate Probability Theory : Probability Primer

• Very good webpage for many courses by A. D. Snider : A. David Snider

• Numerical Methods at University of South Florida and Arizona State University : Instructional Videos for Numerical Methods

• ZFC Set Theory (More oriented around Lambda ...