There are ways to reset the Finder but that's probably not going to help... Check your Login Items in System Preferences for anything that may be causing this. Also check a folder named StartupItems to see if it lists anything that'll be making Finder show on startup.
davidg4781, if you're talking about sleep mode then the machine will come back with everything on the screen in the same position you left it in before putting it to sleep. Shutting down a Mac with a Finder window open shouldn't mean it starts with the Finder window up though.
Yes, I understand how the sleep function works, and that it leaves everything where it is.
I just tried it now, and it worked like I said. I had a bunch of apps open, along with a Finder window. I shut down using the shortcut keys, and turned it back on. Everything was closed except a Finder window, and I don't even think it was where I left it.
Maybe mine's messed up too, but I never thought so. I just have to remember to close the Finder window before shutting down, or close it after it starts back up.
I noticed this first when installing software that needed restarting.
Last week, there were a few times when Finder opened windows that were in use when I initiated a shutdown. This was right after I finally updated QuickTime and iTunes along with a printer/scanner installation and uninstallation. After a couple of shutdown & boot cycles, everything seems to be back to normal. It was a bit annoying when it was happening though.
Actually, I should check it again to make sure it is really gone. I usually close all windows before shutdown, so I may not have noticed it if it started happening again.