Discord lets you join up to 100 servers on a free account, and 200 servers if you have Nitro. Discord’s support page also says that if you drop Nitro after being above 100, you won’t be removed from servers you’re already in, but you won’t be able to join more until you’re back under the free limit.

Extra detail

  • Free account: 100 servers.
  • Nitro: 200 servers.
  • If you already exceed 100 with Nitro and then cancel, your existing servers stay, but the cap still blocks new joins until you go back under 100.

In practice

So the simple answer is: 100 normally, 200 with Nitro.