You want your Email box to be more secure, If anyone guesses your password, Your Email box will be compromised. Currently all the big names such as Gmail,DropBox supports two step verification. Once you enter your username and password they send you a verification code on your mobile device, by entering this code you are allowed to access your account. But for this you need to have mobile coverage or else you will not allowed to sign in.
USB Security Key:
There is one more thread by which you will be able to secure your account, Instead of using mobile verification , you can use USB Security Key device. Connect this device to your USB port and you will be logged in automatically without writing generated codes.It uses cryptography instead of codes.This USB key does not require battery or charging.
How To Register Your Device:
To Register your device go to your account under security tab click on 2 Step Verification and click on security key tab. Click on Register Device Button. Once registered try it out by connecting it to USB port, Enter your credentials, tap on USB device and your are good to go.
But limitations for this are this device is only compatible with Google Chrome.You can not use this device with FireFox. If your are using mobile phone for signing in then also you need to rely on mobile verification.