Adobe has released Flash Player 10.1 where critical vulnerabilities have been identified in Flash Player 10.0.45.2 and earlier versions can cause the application to crash and allow an attacker to take control of affected system.So it is recommended to install latest Flash Player version 10.1 in your Computer.
Installing flash player online these days is much tough task when compared to installing Flash player 10.1 offline, I my self observed downloading flash player from Firefox browser from adobe website downloaded and installed Adobe Download Manager plug-in (getplusplus) and also Adobe Download Manager failed to download and install flash player in my Computer thus it seems much better and easier to use Flash player 10.1 offline installer instead.
Reminding you that installing Flash player 10.1 offline will install flash player for Firefox , Opera,Safari and Chrome browsers but not for other browsers like Internet Explorer.Since IE requires to install ActiveX Control in your Computer.
You can install flash player online for Internet Explorer and other browsers by visiting this page.
Update:Here is offline installer link of flash player for IE (Thanks to CC)