I want to thank the folks that responded to my cry for help. I do have to
admit most people thought I just didn't know what button to use to identify
an object. They didn't understand that the results window was gone from my
view, but the button was there and working.
Jennifer Werner, an instructor from ESRI's Washington DC office came to my
rescue.  We tried a couple options but here is what finally worked:
Right click on an open area on the desk top.  Go to properties, settings and
move your display
settings up a notch.  ex: if current settings are 1024 X 768 move it up to
1280
X 1024.  Apply the settings then go back into ArcMap and try identifying.
What happened was I had  accidentally moved the window out of my display.
This brought the window back.

I also received this thread from Dan McCoy that also discusses this problem
and Jennifer's resolution, as well as the options we tried before changing
my screen's resolution.
http://forums.esri.com/forums/Index.cfm?CFApp=93&Message_ID=116521
Here is my original question: I am using ArcView 8.1 and somehow closed my
Identify Results window in ArcMap. Help does not explain how to restart it
again. I have tried closing down the program, and tried using a different
mxd file, but it is no use. I am sure this is simple but I can't figure it
out  Help!!
Liz Wojdak
GIS Project Manager,
Information Technology Services Division, City of Pasadena
(626)744-6816  (626)396-8531--FAX
lwojdak@ci.pasadena.ca.us
"The man who has no inner life is the slave of his surroundings." - Henri
Frederic Amiel, Swiss critic (1821-1881).