Persisting variables?

I’m sure this has been asked before but I have no idea what search terms to use.

Basically, I want to know what the best method is for changing the values of variables that need to persist amongst all users of my site?

For example, say I have a button that can only pressed 10 times. And not 10 times by a single user during a single session, I mean 10 times between every user who ever visits my site. How would I keep a running count?