I'm on a legitimate site and in order to use one of their interactive calendars they want me to upgrade to Adobe Flash 9 or higher.

I don't see what kind of Adobe Flash Player I have, since when I search for it, nothing comes up. But I must have some kind of it installed, no?

Anyhow, is there any reason I should NOT install/upgrade it?

Download it directly from Adobe - the current version is 10.3 - No reason at all not to upgrade.

Adobe Flash Player Support Center

Inland, thanks for the link. I'm going to upgrade right now.

There are 4 downloads listed; do I install the first one?

Try this one -

Updates by version:
Flash Player 10.3 <-<<
Local Content Updater
Uninstallers

No, click on "Get the latest version" that is besides a red square with a "F" inside and then a new web page will appear. In that new page click on the rectangle that has inside "download now" or something like that

Okay, I'll download from those links!

Zenger,
I didn't see your post until after I'd upgraded the Adobe Flash Player; I think I ended up where you suggested, anyhow.
Thanks.