I am trying to analyze the effects of a particular type of course students can take (3 levels: haven't taken the course, taken one course, taken 2 courses) on college gpa. I'm using hs gpa and SAT scores as covariates. My problem is that my response variable gpa is not distributed normally (which isn't too surprising since 4.0 is our upper bound cutoff).

I thought that the usual regression/ANOVA techniques are no longer valid in this situation. I've tried some transformations (log, sqrt, arcsin(sqrt), inverse) that have all failed to produce normal data. Does anyone have any suggestions about how I can proceed (specific transformations or another method entirely)? Do I even have to be concerned with this problem?

Hello,
As I've understood, many of your data are above a cutoff point making your distribution assimmetrical. ¿Am I right?
My first impression is that, first, some nasty data could be biasing your analyses. Try the following:
-Look for outliers.
-Look for lever cases.
Also, if nothing else works (you tried transformations), you could gather the data which is above your cutoff point and enter them as a new factor ("above-the expected" factor or something like that).

As I said before, I'm quite new at statistics, so, I guess my suggestion is likely to be wrong. Somebody here may help you better and, by the way, may make me know whether and why I'm wrong :-S
Good luck!

PS: I tried once the Box-Cox transformations family. Despite it didn't work, you may wanto to try. Just Google it and you will surely find any tutorial or something. Your first step should be to plot a q-q graph and choose which transformation would make the best.