When you install DX, it installs all DX versions 9/10/10.1/11 etc. Then it is up to the OS to decide what the OS can handle, eg. XP DX 9 Vista 10/10.1 (soon 11 with update) and Windows 7 DX 11. Then it decides which DX it will use depending on the GPU and game. It will automatically choose the highest version that the three components can all support, so you do not need to intervene at all. As said earlier though DX is backwards compatible so if you install it you are set up for all of them.
Here is the latest full installer
Download details: DirectX Redist (February 2010)
And the web updater.
Download details: DirectX End-User Runtime
Don't worry about games installing DX during game installation, that is normal as they just want you to be up to date to support their game. If you are up to date it will just overwrite the same files so it will not hurt anything letting it install DX. It is recommended to actually let it update as most people do not update DX manually that often so letting newer games install it can actually benefit you because it can keep you up to date.