First of all, thanks everyone for chiming in on various solutions. I bumped into this issue after I activated my new iPhone 6. I've tried various methods suggested in this post and here is my finding.
Before I describe my test results, I would like to point out to all readers that there are two different type of Google accounts here.
1. Free Gmail account
2. Business Gmail account
So, depending on which account you have, the solutions suggested in this discussion thread may or may not apply to you. As for my case, I have the free Gmail account. In the past, I could setup my Gmail account on my iPhone 5 using the Exchange server. This is a great offering by Google because my email, contacts and calendar will sync to my phone quickly and automatically. As soon as I activated my iPhone 6, I quickly setup my Gmail the same way that I have been setup over the past many years and nothing work. So, here is my result.
1. Resetting network did not solve my issue - I don't think this matter at all. Your phone needs to communicate to the Google Exchange server. So, it doesn't matter if it's using LTE network or WIFI as long as your phone can access the Internet.
2. It has nothing to do with your 2-step verification security feature either. Yes, if you enable this feature for your Gmail account, you'll need to go to https://security.google.com/settings/security/apppasswords to generate a new device password and use it instead of your normal Gmail password.
3. This is not Apple or iOS issue either.
4. The real answer to my issue is here: https://support.google.com/a/answer/2716936?hl=en. Basically, Google has decide to make the Exchange Sync service only to paid Business account starting January 30, 2013.
Does this mean you're out of luck, right? Not really...
Although you can't setup your Gmail as Exchange Sync Gmail account, you can still be able to setup it as "regular" Google mail account. Just pick Google option when setting up new Gmail account instead of Exchange. Once you entered the correct email address and password for your account, all your email, contacts and calendar will sync to your phone. The sync process may be slower than before.
Hope this helps!!!