I worked in a billing department, and learned to be healthily paranoid about such things. I want to regularly check what I'm billed for. I of course check all my bank accounts' balances at least once a day. All billing emails are marked important in my inbox, and I actually open them.

And of course I give every online service a separate virtual credit card (via privacy dot com, but your bank may issue them directly) with a spend limit set pretty close to the expected usage.