How to Solve the Vista Check for Updates Getting Stuck

Download Links:

REQUIRED:
KB3205638: http://www.catalog.update.microsoft.com/Search.aspx?q=KB3205638 Vista
KB4012583: http://www.catalog.update.microsoft.com/Search.aspx?q=KB4012583 Vista
KB4015195: http://www.catalog.update.microsoft.com/Search.aspx?q=KB4015195 Vista
KB4015380: http://www.catalog.update.microsoft.com/Search.aspx?q=KB4015380 Vista

OPTIONAL (if IE9 is installed):
KB4014661: http://www.catalog.update.microsoft.com/Search.aspx?q=KB4014661

Excellent article that explains solutions to more issues with Windows Update. Affiliate Link