I had the HPIO window opening at startup in tiger.
This was the process I used to correct it then and I have used it just now with leopard after an upgrade and it seems to be working so far.
Credit goes to Peter Rukavina for displaying the steps on his blog at:
http://ruk.ca/discuss/2768
"For those of you who are still having problems getting rid of that pesky "HP Trap Monitor" folder window at starup even after installing the newest version of driver software, I've called HP tech support (1.800.474.6836), and they've helped me solve this issue in 10 minutes.
1) Open up your "Macintosh HD" and find Library > StartupItems > HP Trap Monitor
2) Drag the "HP Trap Monitor" folder to your desktop. This should automatically make a copy of the folder on your desktop
3) Once you have the copy of the folder, drag the original "HP Trap Monitor" folder into trash, but don't empty your trash yet
4) Hold down your Control key on keyboard and click on the "HP Trap Monitor" folder on your desktop and select "Get Info"
5) In the Info window under "Name & Extension," change the name so that it reads "HP Trap Monitor.app" (Type in your computer password whenever requested by your computer)
6) Once you close the Info window, the icon of the "HP Trap Monitor" folder should change from a folder icon to an application icon. Note that the name of it should now also be changed to "HP Trap Monitor.app"
7) Drag the "HP Trap Monitor.app" back into you Macintosh HD > Library > StartupItems
8) When a pop-up window appears, click on "Authenticate" (DO NOT click on "OK")
9) Restart your computer
10) After startup, pop-up window may appear regarding permission. Click on "Fix" and then "Restart"
11) Once your computer restarts again, you should be all set. You can now empty your trash.