How many accounts can I have on RuneScape?

You can have as many RuneScape accounts as you like. However, it is against the rules to use multiple accounts in order to make money or cheat in the game. If you violate the rules of the game with one of your accounts, depending on the severity of the violation, either just the one account or all of your accounts will be banned.

The only rules that apply to having multiple accounts are that you do not violate any multi-account rules such as transfering money or items directly between accounts, you may not log onto the same server with more than one account (otherwise your whole browser will freeze), and that you don't sell accounts.