Having different accounts on Google and want to stay logged in all of them at same time is impossible if you use the same browser. That happens because Google automatically identifies whether any Google Account is already opened and begins to use the same login on all its pages that are open later. However, this is about change.
A new feature that allows multiple Google accounts logged at the same time can already be tested. And, unlike what happens today, an account does not interfere with each other, being unnecessary the need to use different browsers for different logins.
For now, the new feature is limited and only supports Google Calendar, Google Docs, Gmail, Google Reader, Google Sites and Google Code. According to Google, if the user wants to use services that do not supports multiple accounts yet, you must log out of service and login in with the account you want.
The innovation is only available for a limited number of users yet. Check it out if you are able to use it accessing your Google Account settings. If not already, stay tuned. Soon all users will be able to use simultaneous logins.