I develop all my web sites like a lot of web design companies on my local computer. I use a program called XAMPP which is a set of program files that will mimic a Unix server. It is open source software that includes the Apache operating system, MySQL, Filezilla which is an FTP program and Mercury which is an email package. Basically everything you need to test websites before deploying them out live to the world.
Just recently I was not able to update WordPress when a version would become available. The answer, at least in my case was to increase the PHP-execution time. As a default the execution time when you setup XAMPP is 30 seconds. By upping that limit to 90 seconds I was able to solve the problem.
Open the php.ini file which is located in xampp/php directory with a text editor and search for the following line:
max_execution_time = 30
I changed the 30 to 90 and in my case solved the updating problem.

For a good guide on installing WordPress with XAMPP and WAMP see this guide over at WPCity