What is the difference between Cohen's d, ANOVA, and Regression? It is my understanding that ANOVA, Regression, and Cohen's d each measures the distance between means of two or more groups. If that were the case, then what is the purpose of having different methods to measure the differences of groups? Are they functionally different in practical applications?
 A: Cohen's d is a measure of effect size for the difference between two means. It doesn't tell about statistical significance.  It doesn't give a formula. It doesn't tell about the means themselves, only the difference. 
ANOVA and linear regression are the same model as each other, although they look different.  ANOVA is usually used when you are comparing the means of more than two groups (that is, the independent variable has more than two levels, or there are multiple independent variables).  It is a generalization of a t test.
Regression can also deal with that case (through the use of dummy variables). 
We use both regression and ANOVA (despite the fact that they are mathematically equivalent) for both historical and substantive reasons.  Historically, they developed separately. Regression developed first in astronomy and geodesy (finding the size of the Earth). ANOVA developed mostly in agriculture (for testing fertilizers and such). It was some time before people realized they were the same.
Substantively, the output looks quite different from typical ANOVA and regression programs. 
