The Flash Player download from Adobe's main website is not a compete installer. After running it, the installer's first step is to download the rest of itself. This generally isn't a problem, but it is useful to have the full standalone installer if you need to install Flash Player on an offline computer. It can also bypass the Adobe Flash Player Failed to Initialize error that sometimes occurs with the normal installer.

You can find the current version of the full Adobe Flash Player installer for all operating systems at the following link:

http://www.adobe.com/products/flashplayer/fp_distribution3.html

There is a table for 32-bit and a table for 64-bit, which corresponds to the type of operating system you have. Most people have 32-bit operating systems. If given the choice, download the EXE installer instead of the MSI installer, since it should do additional requirements checking.