Six currently. One tab for my daily notes/reminders, Discord, my work/regular email, my "fun stuff" email, my background noise (usually YouTube or Twitch.tv), and then the tab of whatever I'm working on (so this forum right now).
I've got 12 tabs open currently and I would say this is a pretty typical amount for me. Right now 5 of them are books that I might borrow from the library and 2 are youtube videos I want to watch later.