God's statue

Basics
At various places around Tyria you can find statues of the 5 Gods:
 * Balthazar - God of War and Fire
 * Dwayna - Goddess of Life and Air
 * Grenth - God of Death and Ice
 * Melandru - Goddess of Nature and Earth
 * Lyssa - Goddess of Beauty and Illusion

Some of the statues are whole, some are broken (especially in ruined post-searing Ascalon).

Note: Also in some rare places you can find beautiful murals of the 5 gods, although these are eyecandy only, and have no function.

Statue Status
The statues change their appearance depending on whether your territory has the Favor of the Gods. If yes, then the statues become "active" and you may interact with them, otherwise they are "inactive":
 * All broken statues become whole.
 * Balthazar: Statue will be burning with flames.
 * Dwayna: Statue will have water running between its pieces.
 * Grenth: Statue will have white mist flowing from it.
 * Melandru: Statue will have water flowing through it.
 * Lyssa: Statue will have a golden light (with glittering sparks falling) at the base and her figure will be lit with a white light. Without the favor, the statue will be dim and there will be thorns engulfing her figure.

Gods' Avatars
If a statue is "active" (this means if your territory has the Favor of the Gods) you can summon the god's avatar at his statue. You do this by walking up to the inscription at the statue base and typing "/kneel" in console.

Avatars in explorable areas offer the following blessings in exchange for offerings:
 * Offering to Conquest(50 gold): Dwayna's Blessing - a health regeneration enchantment similar to Mending
 * Offering to Courage(100 gold): Morale Boost +2% or reduction of Death Penalty (if you have any)

Avatars in the Temple of the Ages offer access to the Realms of the Gods. Avatars in other outposts sometimes offer quests.

Known Statue Locations
It is worth mentioning that the entire regions of the Crystal Desert and the Ring of Fire Islands being inhospitable to civilization, do not feature any statues made to the gods either in outposts or in explorable areas. Also, the Shiverpeak Mountains do not have any statues in outposts since the Dwarves worship the Great Dwarf and not the Old Gods.

Balthazar

 * Old Ascalon (east of the entrance to The Breach)
 * The Falls (near the eastmost end, next to Meghan the Bright)
 * Temple of the Ages (avatar gives you access to the Fissure of Woe)
 * Majesty's Rest (on the eastern side, at entrance to the island of Bone Dragons)

Dwayna

 * Sardelac Sanitarium (avatar gives quest Family Ties)
 * Serenity Temple
 * Temple of the Ages
 * Druid's Overlook (avatar gives quest Wisdom of the Druids)
 * Dreadnought's Drift (southeastern corner, beware of Wurm)

Grenth

 * Ascalon Foothills (near Traveler's Vale entrance)
 * Diessa Lowlands (northwest, near Ascalon Foothills entrance)
 * Lornar's Pass (southern end, west of the entrance to Dreadnought's Drift)
 * Temple of the Ages (avatar gives you access to the Underworld)

Melandru

 * Regent Valley (King's Watch)
 * Serenity Temple
 * Temple of the Ages
 * Tangle Root (southeastern tip, near Old Joness)
 * Twin Serpent Lakes (north-western end)

Lyssa

 * Temple of the Ages
 * Eastern Frontier
 * Old Ascalon (northwest of the Ascalon City main gate, half way to the entry to The Breach)
 * Mineral Springs (inside Ice Imp cave at the northeastern tip of the area)