Those improves your coding ability a lot. For example, If your application needs to scale well, you should always consider implementing efficient algorithms. Yes, you can use some open source libraries, tools, etc but someone has to write those using efficient algorithms. This is one of the main reasons, that companies like Facebook, Google are recruiting people using these "puzzles" or contests like Topcoder, Google Codejam.
I think these kinds of problems make you comfortable with algorithmic thinking, it may not always be necessary to implement algorithm X or whatever in your day to day code but being comfortable with algorithms (by practicing) means you don't push off or miss the correct times to implement algorithm X.
