2 - Ancestor Worship (+1 Culture for every Shrine) - Primarily, this is useful if you're the Maya and going for a super-shrine strategy, and then otherwise don't intend to spread your religion beyond your empire. In fact, that's likely what super-shrines are best for, if you want a little bit of use off a cheap religious building when you only want to use religion defensively. It's good for that, especially since Shrines are cheap and a little bit of Culture never hurt, but you probably don't want this if you're going super religion.
3 - Dance of the Aurora (+1 Faith from non-forested Tundra) - This one is basically Desert Folklore for Tundra starts. If you do get a start up north, it's definitely worth it, since it makes your surroundings give you a load of Faith. But I find Tundra starts are a bit rare, honestly.
5 - Desert Folklore (+1 Faith from Desert tiles) - Arguably the single best Faith generating Pantheon in the game. If you start in a desert, GET IT, or hell, if you start anywhere near a desert, still maybe try to get it. That Faith racks up FAST, and swiping this alongside Petra is a quick path to being extremely powerful throughout the game. Morocco especially wants this what with the Kasbah and everything, as they can quickly turn unworkable desert tiles into an absolutely immense base.
3 - Faith Healers (+30 HP healed per turn if next to a friendly city) - This one is probably one of the better Pantheons to take if you're going war, mostly if you only intend to spread religion a little. It can be a good strategy to send Missionaries out to key locations where your troops are going to base an assault from, and use that city as a base to rapidly heal your troops and swiftly send them back into the front lines. Pays off best if you end up in tight borders with someone else and are likely to fight a long war of attrition and holding the line.
2 - Fertility Rites (10% faster growth rate) - I'm not exactly sure of the best way to use this one. It definitely pairs well with the Temple of Artemis, yes, which entails you want this if you're going for a semi-wide strategy with lots of tall cities, but hmm. It seems a little tough to make best use of, mostly for if you're founding lots of key cities but don't intend to found a religion. But I feel that a wide empire could make religion very powerful, and there's better Pantheons for it anyway.
1 - God of Craftsmen (+1 Production in cities with population of 3+) - The best way I can see to use this is if you intend to go Order and Resettlement and go for serious ICS, but then, 1 point of production is still pretty weak, and to make real use of it you probably need missionaries anyway, regular use of which necessitates a high faith yield that could be done for other things.
2 - God of the Open Sky (+1 Culture from Pastures) - Best useful if you're Mongolia, the Huns, or Poland, or otherwise have lots of Horses or other Pastures available. It's pretty simple and useful, but somewhat situational, and in the long term won't yield as much as one would want.
4 - God of the Sea (+1 Production from Fishing Boats) - The pantheon to take if you've got a heavy sea bias. Carthage, England, Venice, starting by ocean resources in general, this is a belief that is very useful both early game and later on, especially with Offshore Platforms. Of course, if you're landlocked or there's no locations with large amounts of water resources...maybe you want to pick something else, but if there are lots of boats in your future, definitely go for it.
1 - God of War (Gain Faith if you win a battle within 4 tiles of your city) - This just seems...a bit meh. It functions best when you've got Barbarians swarming you or hostile neighbors, and...I really don't think a belief that relies on people coming in to take your stuff is very reliable. If you see a long war of continuous invasion in your future, consider it, but otherwise...
4 - Goddess of Festivals (+1 Culture and Faith for each Wine and Incense) - Stacks awesomely with Monasteries. If you have lots of those resources available, this is a super awesome belief and you should definitely take it.
2 - Goddess of Love (+1 Happiness from cities with population of 6+) - Like with God of Craftsmen, I'm not sure how to really use this, and it seems a little weak for what you would intend to use it on.
3 - Goddess of Protection (+30% increase in city Ranged Combat Strength) - Probably the best one to get if you're trapped by hostile neighbors or will otherwise likely get into a dangerous war. Of course, doesn't do much when you're at peace, and not exactly something reliable since you can still get your stuff taken if you get this, but it's definitely a huge boost.
3 - Goddess of the Hunt (+1 Food from Camps) - It can definitely be a big yield, but I find I never start by enough Camp-based resources for this to be of much use. I have used it before though, and it is definitely a help, especially since this likely takes best effect in an area where Food is otherwise low.
4 - Messenger of the Gods (+2 Science in cities with a Trade Route) - It can definitely be powerful, especially if your empire is going wide and you intend to build lots of roads. Works very nicely for the Maya or any science-based civ really, and can be a huge chunk of science early-game.
3 - Monument to the Gods (+15% Production of Ancient/Classical Wonders) - If there is a Wonder you REALLY REALLY NEED then this is a good one. A viable strategy with Rome since you want a lot of wonders as them and they're all over the tech tree. Obviously this has the best effect as Egypt, especially if you've got a decent production base and Marble available, as you'll be pumping out Wonders faster than Monuments at that rate.
3 - One with Nature (+4 Faith from Natural Wonders) - If you're Spain, you want. Otherwise, a bit unreliable.
3 - Oral Tradition (+1 Culture from Plantations) - Can be nice, but a little situational. It's basically a Goddess of Festivals light if you have lots of plantations in your future.
3 - Religious Idols (+1 Culture and Faith for each Gold and Silver) - Basically a different version of Goddess of Festivals. If you have these around, go for it, it will pay off a lot.
1 - Religious Settlements (+15% faster border growth) - ...eh. If you're Russia or the Shoshone, you can gain a lot from this, but otherwise...
5 - Sacred Path (+1 Culture from Jungle tiles) - Anyone with a Jungle bias will have a field day with this. That bonus is huge when applied to nearly every tile, and combined with Trading Post spam it can do a hell of a lot.
2 - Sacred Waters (+1 Happiness from cities on rivers) - ....eh.
4 - Stone Circles (+2 Faith from Quarries) - Links well with the Mausoleum, and can get a lot of Faith in general. I find large concentrations of Stone somewhat rare though.
4 - Tears of the Gods (+2 Faith from each Gems or Pearls) - Requires an odd terrain, but can be extremely powerful. Gems seems a bit rare to me though, I never seem to start near it.