I have to say so far I am not impressed with the Gods and Kings expansion for Civ V. Keep in mind I am slow to embrace change.
The good:
I like that City States give missions with expiration dates now; previously you could court a city state for a while and then they would demand you kill another city state and if it just wasn't practical for you to do (because it was protected by another civ or was just too far away) that was that, the only way to gain favor was to gift them gold for the rest of the game. They would hold that grudge for 1500 years and until someone killed them there was nothing else they wanted. Now they only ask for you to "bully" city states and if after 30 turns no one has done it, they just give up. In addition they have new "quests" to be the civ with the most scientific progress in 30 turns and the like.
Unit HP and DMG have been multiplied by 10. This means there is more variation in the attack you can do and that bonuses to attack and defend work better. Instead of a unit doing 1 DMG per hit, getting a +20% to attack bonus, and still doing 1DMG for the next 4 turns it goes from 10 to 12.
The Meh:
Religion seemed neat at first, but, other than getting to choose some bonuses for cities with your religion, and yourself as the founder, I don't see what the point is really. Once the religion is founded all you can do it spread it, which is good if you have a "founders bonus" that is based on the number of cities which follow it, but other wise does nothing. Having another civ follow your religion has not effect on your diplomacy with them, though trying to convert the cities of another founder does have a negative impact. So my bonus is +1 happiness for every 5 followers in a converted city. Converting cities is all I can do with "faith" points once the religion is founded it hardly seems worth the diplomatic toll to get +1 happiness, particularly since if the civ has their own religion they will just convert back.
Spies. I never loved spies in IV, but it was easy enough to just defend against them. I am unclear how I am awarded spies in V. I think you get them at the beginning of eras starting with the Renascence, but I feel like the AI civs have more than me? Maybe I am just bad at using them, but I feel like I am not getting anything but frustration from the spy system.
Bad:
One of my advisers is broken? I think she cannot see the happiness I get from my religion, so she is constantly warning me that my people are livid when I have positive happiness.
AI keep warning me that another AI is "plotting against me" which is info one can gain with a spy, but I don't see how they are. For instance I was warned that Montezuma was gathering an army to attack a specific city but I could see that he was not, and he never attacked. I don't think there is a mechanism for lying about the info gathered, it is just optional whether to tell the Civ or not. The info seems useless, but it is supposed to be a great diplomatic thing that they shared this with me.