Pretty much all of the common statistical models we use, with the exception of OLS Linear Models, use Maximum Likelihood estimation.
This includes favorites like:
All Generalized Linear Models, including logistic, probit, Poisson, beta, negative binomial regression
Linear Mixed Models
Generalized Linear Mixed Models
Parametric Survival Analysis models, like Weibull models
Structural Equation Models
That’s a lot of models.
If you’ve ever learned any of these, you’ve heard that some of the statistics that compare model fit in competing models require that models be nested. This is particularly important while you’re trying to do model building.