Google Software Engineer Hari Nidumolu says that checking his two different accounts used to mean he had to sign out and back in to Gmail all the time, but no longer.
Instead, with Gmail's New Email Delegation Feature he can grant personal account access to the other account and view, organise and send mail without the erstwhile logout/login hassle.
In a blog post, Nidumolo notes that Gmail has offered email delegation for Google Apps accounts for some time targeted to users people who want to authorise assistants to access to read or respond to mail on their behalf, but this this functionality is now available for anyone using Gmail.
To grant access to another account, click the Settings link in the top right corner of the Gmail UI window. On the "Accounts" tab, you'll see a new section where you can "Grant access to your account."
The account you add will receive a verification email with links to accept or deny access. Once the account accepts and you've refreshed your browser or logged in and out again, you'll see a small down arrow beside the email address at the top right corner of Gmail which can be used to toggle between accounts.
Each account will open in a different browser tab or window, so you can view both accounts simultaneously, all while signed into your primary account. When you send a message from one account while signed into the first account, it will appear as being sent by the primary login account on behalf of the secondary account.
Signing out of any one of the accounts will sign you out of all the accounts you're currently viewing, and, of course, you can revoke access at any time.
Google has posted a how-to video here.