Ever since I updated to KitKat on my S4, Google kept asking me to sign in to allow Gallery to access Picasa Web Albums or something like that. Every time I open Gallery it would come up. Despite saying "No" and removing the notification, it just came back every time.
To remove this notification, I went into the Gallery (the stock gallery app) and hit the menu button (the capacitive button on the bottom left of the phone), went into Settings. I tapped my gmail address under "Accounts" at the top and scrolled to the bottom of that list. Once I unchecked "Sync Picasa Web Albums" the notification stopped appearing. Not sure if this was some update within KitKat or not because I never had the notification before.
Anyway, I decided to post this so anyone with the same issue who tried searching for it might find this and it will help them.