How do you do that?

Pings by people and groups can't be, to my knowledge. Pets being checked out of the resorts can't be disabled, same for training times and events for site events. Everything else I think can be, I'm not sure, I never saw the need.

For alerts for games and stuff, you can choose to just not set the alert when you're done. I don't think there is a way to turn off alerts for comments or forum pings by individuals, but you actually can turn off group pings. If you go to the forum group page for that group, there will be an option to turn off notifications.

Shop sale pings can be turned off as well, if you go to edit the shop and select "no" for Receive Events. That's all I can think of off-hand.