I have activated two steps verification on my GMail and soon after that, i couldn't access my GMail account through my phone. I just realized that some third party applications hasn't supported this feature yet, so they need a special treatment.
GMail provides application spesific password which can be generated by going to your Google Profile and pick the two steps verification and go to the bottom of the page. Please give a name to the new device or application that you want to be connected to your GMail and it will generate OTP (one time password) that you should enter on your device/application. After re-authenticating, everything works normally again.
I hope this helps for those who have activated two steps verifications. It's a little bit uncomfortable at first, but when you get used to it, you will get the security benefit out of it.