Ping is built into iTunes & cannot be removed by way of settings/preferences. But if you feel comfortable with using Terminal, you can remove the Ping elements from iTunes with these commands.

This will remove the drop down button/menu that appears next to each track.

defaults write com.apple.itunes hide-ping-dropdown -bool YES

This will remove Ping from the sidebar.

defaults write com.apple.iTunes disablePingSidebar 1

Yeah.. Open up the Terminal in Applications/Utilities and type and hit Return. Restart iTunes and the buttons should be gone.

defaults write com.apple.iTunes hide-ping-dropdown -bool TRUE

And for good measure run this too:

defaults write com.apple.iTunes disablePingSidebar 1

That should pretty much hide Ping from you.

Edit :: And what rpm said.

Here is the Windows equivalent to the Mac OS answers above:

32-bit
“C:\Program Files\iTunes\iTunes.exe” /setPrefInt hide-ping-dropdown 1
“C:\Program Files\iTunes\iTunes.exe” /setPrefInt show-store-link-arrows 1
“C:\Program Files\iTunes\iTunes.exe” /setPrefInt disablePingSidebar 1

64-bit
“C:\Program Files (x86)\iTunes\iTunes.exe” /setPrefInt hide-ping-dropdown 1
“C:\Program Files (x86)\iTunes\iTunes.exe” /setPrefInt show-store-link-arrows 1
“C:\Program Files (x86)\iTunes\iTunes.exe” /setPrefInt disablePingSidebar 1

I copied that from this discussion
http://discussions.apple.com/thread.jspa?threadID=2593347&tstart=0

They also say you can simply disable the iTunes store in Parental Controls.

Thank you, everyone!