The buttons cannot be disabled in the UI, but there's a Terminal fix to do it.
First, quit iTunes just in case. Then, start Terminal.app and enter:
defaults write com.apple.iTunes hide-ping-dropdown 1
When iTunes is restarted, the Ping buttons should have disappeared. To reverse, just repeat, using '0' rather than '1', or alternatively delete the setting altogether to ensure default behavior:
defaults delete com.apple.iTunes hide-ping-dropdown
Unfortunately, the old 'show-store-arrow-links' hack no longer works. However, it turns out the setting has just changed to 'show-store-link-arrows' and now defaults to off to allow for the default Ping buttons. To restore the arrows:
defaults write com.apple.iTunes show-store-link-arrows 1
Combine this with the invaluable 'invertStoreLinks' setting:
defaults write com.apple.iTunes invertStoreLinks 1
Now the arrows will cross-reference within your own iTunes Library. Far more useful than either Ping or the iTunes Store!
[crarko adds: I tested this, and it works as described. Four people submitted versions of this hint with 24 hours of the release of iTunes 10.0.1. This one was first. Note that you can freely substitute TRUE for '1' and FALSE for '0' in any of these commands, and changing the values back to 0 will restore the original setting given by Apple.]

