How do I control Emacs’s case-sensitivity when searching/replacing?

The value of the variable case-fold-search determines whether searches are case sensitive:

(setq case-fold-search nil) ; make searches case sensitive
(setq case-fold-search t)   ; make searches case insensitive

Similarly, for replacing, the variable case-replace determines whether replacements preserve case.

You can also toggle case sensitivity at will in isearch with M-c.

To change the case sensitivity just for one major mode, use the major mode’s hook. For example:

(add-hook 'foo-mode-hook
          (lambda ()
           (setq case-fold-search nil)))