Practical application of Finite State Machines
Each time you do a search (particularly a "pattern search") in your favorite editor/tool, the pattern is translated into some form of finite state machine, which does the matching.

The lexical analysis part of your compiler/interpreter (yes, even your shell) is again a finite automaton which matches keywords and other tokens recognized by the language.

Any vending machine is a finite automaton which takes in coins of different denominations and recognizes when the correct amount has been entered (OK, today's vending machines probably have a small CPU inside doing the adding, but the end result is the same).