This issue can be exacerbated by anti-virus/internet security applications blocking Steam from doing what it wants to and reading all of Steam's files as the Steam application attempts to verify them.Try adding exceptions in these applications for your Steam folder and restart Steam to see if this resolves your issue.If the window appears every single time you start up Steam, you're probably experiencing an issue with Steam realising it has updated.It's worth noting that this is a well discussed issue with no official solutions available, there are plenty of different suggestions on how this can be fixed though and some of these work for some of the people experiencing the problem some of the time, so you'll want to try all of them if you really want to stop Steam from verifying every time you start it.
If is down for us too there is nothing you can do except waiting.
What you'd do here is wait however long it normally takes to verify files and get into the main Steam interface, and then close Steam with the menu option (or system tray icon) before restarting it.
After restarting in this manner, the file verification window shouldn't appear, since Steam would have properly closed all of its files when it exited.
The blue bar displays the response time, which is better when smaller.
If no bar is displayed for a specific time it means that the service was down and the site was offline.