Some things (like babies) are easy to count, but some things (like coughs) are definitely not! Matthew Rudd uses these two examples to talk about regression for counts, along with several current real-world applications.
Once you've built a regression model, how do you know if it's any good? For linear regression, a standard and often-misunderstood diagnostic is the coefficient of determination; for logistic regression, a great diagnostic that should be much more widely known is the coefficient of discrimination.