Google has recently announced a new feature that allows anyone else to delegate your email on your permission. This feature does not require you to give away your email username and password and has been available for quite some time on Google Apps.
All you need to do is go to Settings -> Accounts and import -> Grant access to your account, which can be seen on scrolling down the page.
Once you enter the email ID (necessarily a Google ID) and setup an account for access, you can operate two accounts in the same browser simultaneously and this allows you to send and receive mail as the second account. Needless to say, use this feature only with people you trust the most.
Signing out of any one of the accounts will sign you out of the primary account. This official video explains this feature better.