Altars

Altars can be found in various locations in the dungeon. Altars are specific to one of three gods: Altars can be used to make sacrifices to the corresponding god. The more sacrifices you do, the more you will be in favor of that god. Some times you can make multiple sacrifices to the same altar. Though some times the altar gets bugged and will accept hundreds of sacrifices and never give any rewards, in my opinion, to avoid this, save and reload after each sacrifice on an altar (if it is bugged the bug gets removed after reloading) or only do a max of 2 sacrifices per altar.
 * Lady Sophie (green altar)
 * Density (yellow altar)
 * Grievous (red altar)

Having one god in your favor gives various benefits. Some floors that are "sacred" ground to a god, will be easier. For example, grievous sacred ground will spawn flesh golems and blood imps if you are not in his favor. Lady Sophie sacred grounds will spawn wardens or dryads or phantom blades if you are not in her favor. Some places you can pray and get a god blessing, if you are not in favor you get nothing or you may get attacked by summons. You also get better chances of getting rewards at their altars if the god is in your favor. Healing water will have extra healing properties if you are in favor of Sophie and you can use healing pools as a life potion if you are on her favor.

Grievous and Sophie hate each other. Sophie will almost never help or give rewards you if you have more offerings to grievous than her. Grievous is less bitter if you have sacrificed to Sophie before, he is more likely to give rewards even if you are more in Sophie's favor.

There are also some special chests with a good item in it, you can grab the item in the chest but you get cursed by a god. And then you need to do a sacrifice to that god if you want to remove the curse.

There are rare sprites that have special effects based on Sophie or Grievous. Red sprite may summon a wraith (if you gater it with another red sprite in a room) and to other stuff (for know is unknown) the white sprite which is VERY bright will scare shadow imps.

Praying for help
The gods (usually the one you are more in favor) will help you if you get stuck. They can teleport you out to a random location if they feel you are trapped. Or they can open locked/barren doors.
 * If you are low on health with no healing items, praying to Lady Sophie can result in you being healed.
 * Lady Sophie never ask for any payments.
 * Density takes 12 gold each time he helps you.
 * Grievous will not ask for anything the first few time he helps you, but the more you request his help, the more payment you have to give. He wants to see a fight as entertainment, wants to see blood being shed. Thus he summon monsters so you battle them. Thew more you ask for help the more monsters he summons and the stronger they get. After many prayers eventually he will summon 30 flesh elementals, which are strong enemies with high HP and high life regeneration.
 * In some rooms you can pray to grievous or Sophie to get unknown rewards. Red rooms with blood and torture devices is Grievous room. Green rooms (usually with a well) is a Sophie room. Grievous gives the Enraged buff (+3 strength and +2 speed) if you pray near enemies. Sophie may destroy turrets if you pray near a turret.

What to sacrifice in Altars.
Red Altars (Grievous)
 * Small Sacrifice: Flask of blood, orc tooth, weapon with less than 10 kills.

Possible Rewards: A single healing potion, 2 Incineration potions, 2 explosion potions, cursed weapon or a +1 weapon.
 * Medium sacrifice: Orc necklace, spider queen fang, weapon with 10 or more kills but less than 25 kills.

Possible Rewards: Death or fire sigil, 5 explosion potions, cursed weapon or +2 weapon.
 * Medium sacrifice: Ogre heart

Rewards: Uncursed. If you are not cursed, you can get death or fire sigil, 5 explosion potions, cursed weapon or +2 weapon.
 * Big sacrifice: White wyrm spine, living heart, weapon with 25 kills or more.

Possible Rewards: Vampiric weapon, bow of draining, bow of poison, shield of firestorm, weapon of fire, weapon of despair, staff of fiery doom, cursed weapon. Pretty much, he accepts weapons with kills or monster remains.

Grievous does not accept bloat glands.

Verification needed if he accepts, fire ant glands, troll blood, queen bee stinger and other monster loot as sacrifices.

Yellow Altars (Density) 
 * Small Sacrifice: Lockpicks, tools, made of marble, iron, sulphur, saltpeter.

Possible Rewards: May uncurse, hasted, strengthened or invisibility buff.
 * Medium sacrifice: Made of amber, silver or gold, mithril piece.

Possible Rewards: May uncurse, earth or metal sigil, +1 ring, 2 skill stones, potion of strength, medium duration hastened, strengthened or invisible buff.
 * Big sacrifice: Mithril treasure worth 500 gold.

Possible Rewards: May uncurse, weapon of force, weapon of mastery, dagger of return, bow of lightning, ward crushing, shield of shattering, ring of stone skin, long duration hastened, strengthened or invisible buff. Pretty much, the more valuable the item, the better the chance of getting good rewards.

Verification needed if he accepts meteoric iron.

Green Altars (Lady Sophie)
 * Small Sacrifice: Ration, tea leaves, healing water, holy Water.

Possible Rewards: Always uncurse or blessing (you take half damage while blessed)
 * Medium sacrifice: Made of jade, tea, potion of Healing.

Possible Rewards: Always uncurse, life or water or magic sigil, 2 enchanting scrolls, 6 light scroll, 3 remove curse scrolls, potion of life, medium duration blessing.
 * Big sacrifice: Potion of life.

Possible Rewards: Always uncurse, cloak of mending, weapon of purity, dagger of disarm, ward harm, ward slashing, shield of blazing, shield of absorption, long duration blessing.