Are you getting the download from Adobe.com or another website?
I've got a 64bit Windows 7 system and go direct to the software vendors for downloads. When I click on what I want the site will detect it's a 64bit system and what OS it's running too. Sounds to me like you may be trying to install the 32bit version of Acrobat Reader on your computer. The vendor's webiste can detect what version of Windows you are running and should download the appropriate version of their software when you click on the link you want.
I know Adobe Reader takes a while to install. Could it be possible you are somehow aborting the installation before it's finished? Also, you're not trying to install Adobe Acrobat as opposed to Acrobat Reader, are you? Acrobat is not free where the Reader is. Acrobat can be purchased as a standalone application or part of one of Adobe's Suites. I am an Adobe Reseller, a member of NAPP, and use Adobe's software a lot. The only time I will get an error message is if I happen to try to install 32bit applications on my 64bit machine (not those that can be detected by the vendor website). Even Apple's Quicktime/iTunes has 32 and 64bit versions and the Apple website detects 64bit on my system.
Hope this helps some.