There's a lot of great stuff out there. It's hard to narrow it down unless I konw what field you're looking to work in. However, I do have a few suggestions.
First, to answer your question about what's next after Regression... well, there's a lot. However, in order to get to the meat of stuff like multivariate regressions, supervised/unsupervised learning, time-series analysis, survival analysis, simulation, PCA, clustering, etc. etc. there's A LOT of pre-req work that should be looked at in both mathematics and computer science.
Personally, I think that one of my favorite progressions in my stats training has been acquisition of the R language. Though I studied stats in college and was exposed to R and SPSS a few times during my BS, there's so much stuff out there now for R related to stats.
The best starting point, IMO, would be Data Camp's Data Analysis and Statistical Interference with R class (free): https://www.datacamp.com/courses/data-analysis-and-statistical-inference_mine-cetinkaya-rundel-by-datacamp
If you find this valuable, there is an even longer (but not free) Datacamp course offered by a Princeton Professor (Andrew Conway) called "A hands-on introduction to statistics with R."
Second, I would recommend checking out both EdX and Coursera. Right now I'm enrolled in an excellent EdX class on statistics (also using a bit of R) called Foundations of Data Analysis (offered through University of Texas): https://courses.edx.org/courses/UTAustinX/UT.7.01x/3T2014/info
Another MOOC option (this one through Coursera) is: John's Hopkins' Stat. Inference class (this one is part of a longer Data Science Specialization, which you may be interested in); however, this specific class definitely involves more advanced stats than the Udacity class.
MIT OCW might have some stuff as well.
Basically there are two main branches of stats before you get to higher level stuff:
- Exploratory Data Analysis
- Statistical Inference
I would search Google for those two subjects to find more classes related to this stuff.
When I was in college after the first few intro stats classes, I was introduced to more advanced ways of looking at the same things by taking Probability and Statistics courses through the math department. These classes were VERY intense--they required the knowledge of calculus and linear algebra; however, as I've progressed in the field, knowing the mathematical derivations of this stuff has saved me a lot of work.
Ultimately courses like Econometrics and Decision and Risk Analysis used tools that I was introduced to in intro stats and honed in math. With that background and a little bit of computer programming (R is a great place to start--or Python's Pandas), I would say you'd be pretty much ready for anything advanced--such as machine learning.
The bottom line is that there is PLENTY of free stuff available online :)
Best of luck!