The speed with which you need to do this and the extent of it will depend on how much you use your phone for online interaction. For some, this may be very little, while for others, it could be a huge task. You may also want to cancel any credit/debit cards that were registered to any online stores through that device (like the App store, for example).
If you're worried that the phone is in someone else's hands, the sooner you do this the better, as identity theft is a serious and widespread issue. It's better to take the time to reset your passwords and logins before physically hunting further for your phone. This will minimize the potential damage someone could do with access to your information, and if you do find your phone then using new passwords is only a minor inconvenience. Start with your most important passwords. This typically includes email, bank accounts, Facebook, and online storage. Deal with financial and personal information first. After you have changed your major passwords, you can reset passwords for less important services.