Can you open Reader standalone (without opening a file)?
If so do that and try help>Repair Adobe Reader installation.
That would be the easiest thing to try.
If it doesn't do the trick, you can try some of the suggestions at http://kb2.adobe.com/cps/328/328924.html. There are a ton of them. Even though it mentions Acrobat, a lot of the suggestions can be used for Reader as well.
I did try opening Reader without opening a file and it still hung.
Thanks for suggestion to look at the postings at http://kb2.adobe.com/cps/328/328924.html
In the meantime, it seems that the problem has resolved itself. I needed the Reader to work with fillable form files from the NIH that have imbedded pdf files attached to them. I can open the files with Preview but can't get at the attachments. I just dumped one of the files into Safari and everything works as it's supposed to with Adobe Reader including being able to click on a tab and have an attachment pop up. If the attachment is a pdf file, then it calls Adobe Reader (which I had set as my default pdf reader). At first it looked like the Adobe Reader window with the file was hanging as usual. After a short time though, the file had been opened and the Reader was no longer hung. And NOW when I try to open any other pdf files with Adobe Reader, there is no problem. I don't understand it but I'm glad it's now working.