Categorical regression analysis: Undertakes multiple regression when some of the variables are ordinal or nominal.
Nonlinear Principal Components Analysis: Undertakes conventional principal components analysis, when some of the variables are ordinal.
Nonlinear Canonical Correlation: Undertakes canonical correlation when some of the variables are ordinal and nominal.
Correspondence Analysis: Undertakes something like a factor analysis on two categorical variables.
Homogeneity Analysis (also called Multiple Correspondence Analysis): Undertakes something like a factor analysis on more than two categorical variables.