Syntax highlighting. The Scite text editor allows you to write your own lexer (in C++) to provide syntax highlighting for any custom language. I wrote my own custom lexer for Scite as a refresher on this topic (I studied it a while ago at university).
Regular Expressions are often used as an alternative for pattern matching and simple language processing. This is even more common of recent years thanks to the improved RegEx support in frameworks such as .NET. In many cases developers may not even know of lexing/parsing techniques and so fall into usng Regex by default.
However, as another answer says, Regex can quikcly become inefficient,slow and difficult to maintain for anything more then a simple grammar/language. In that situation parser/lexers are generally the best choice.