go to settings>accounts. tap on your google account, and double check everything is selected that you want to sync. Try un-checking and then re-checking an item to force it to sync. IF you are still having problems, REMOVE your Google account (you won't shouldn't loose any data) and reboot. Re-add your Google account. Let the phone sync for a few minutes. If your email doesn't start coming in, go to the Gmail app and make sure you're logged in correctly. Again, it may take a few minutes for everything to re-sync after removing and re-adding your account, so patience will be helpful.
**EDIT** my account was acting up today too, despite trying 2 different WiFi networks and mobile data. Everything else worked fine, but Google stuff wasn't syncing like it used to. I removed my Google account (and cleared the phone's cache just for good measure) before rebooting and re-adding the account. It took about 20 minutes for stuff to start syncing again, but normally it only takes a minute or 2