Optional Dungeons

In the Golden Sun series, there are various dungeon-style locations that are not mandatory to complete for the sake of reaching each game's ending. This includes one main one in the original, and four main ones in the Lost Age.

Golden Sun optional dungeons
Golden Sun has several dungeon-style locations throughout the game

Fuchin Falls Cave
Fuchin Falls Cave, located within Fuchin Temple, can be entirely skipped, though you will not gain the Orb of Force, the Arctic Blade, or the Jupiter Djinni Zephyr.

Vale Cave
Vale Cave, located within Vale, is more of a "hidden dungeon", and a somewhat small one; it contains the Halt Gem and the Jupiter Djinni Kite.

Vault Cave
Vault Cave, located within Vault, is another "hidden dungeon" very close to Vale and its cave, which going through allows access to the Vambrace and the Venus Djinni Sap.

Gondowan Cave
Gondowan Cave, the two entrances of which are located southeast and northeast of the Karagol Sea, is a location that serves as a pathway allowing the player to travel back and forth between the Tolbi and Kalay sides of the Karagol.

Lunpa Fortress
Lunpa Fortress, located within Lunpa, is a more complex dungeon that is relevant to a subplot in Golden Sun, complete with its own boss battle, access to the Mythril Circlet and the Mercury Djinni Tonic, and opening up the weapon and armor vendors in Lunpa.

Crossbone Isle
Crossbone Isle is the hidden, optional "super-dungeon" of Golden Sun that is intended to be a greater challenge than even the final mandatory dungeon. It consists of nine puzzle-filled, random-encounter-free floors, each level being guarded by at least one powerful "mini boss" enemy at its door, and all sorts of powerful and unique equipment can be found there, as well as the Venus Djinni Bane. At the bottom is the encounter with Deadbeard, the first game's resident "optional superboss", and defeating it earns you the Demon Mail.

Golden Sun: The Lost Age optional dungeons
Despite this game being much longer than the first one, it has somewhat less of an emphasis on dungeons that are optional over the course of the main game and far more emphasis on optional, challenging late-game dungeons. (It could be said that this is a main reason why the second game is much longer.) This does not include the various one-room cave locations that contain single puzzles that reward you with Summon Tablets.

Madra Catacombs
Madra Catacombs, located in Madra, is an underground area with a couple key collectibles - the Tremor Psynergy, which is helpful but not mandatory to completing the game, and the Moloch summon. Various aspects of this area become explorable over time, but you need the Frost and Reveal Psynergy to loot it fully.

Alhafran Cave
Alhafran Cave, located in Alhafra, is a small underground location first accessible only by giving the Large Bread to a hungry kid in town, so that the father guarding the entrance lets you pass. It most notably contains the Ixion Mail.

Gabomba Catacombs
Gabomba Catacombs is essentially an optional "second half" to the mandatory "first half" known as Gabomba Statue, located within Kibombo on Gondowan. It can only properly be explored and cleared later on, though, after getting the Cyclone Psynergy. It contains, most notably, the Tomegathericon class-changing item.

Taopo Swamp
Taopo Swamp, located southwest of Yallam on the continent of Osenia, is a large and multi-segmented location with above-ground, cavernous, and volcanic areas. Collectible are two Tear Stones and one Star Dust forgeable material, as well as the Venus Djinni Flower.

Izumo Ruins
Izumo Ruins, located in the town of Izumo, is an underground dungeon that can only be properly explored with the Sand Psynergy. Notable collectibles are the Phantasmal Mail and the Ulysses summon sequence.

Treasure Isle
Treasure Isle, the island located in the northeastern area of the world map, is one of the four main optional late-game dungeons, though parts of it can be explored earlier on in the game. The most noteworthy feature, even beyond the large amounts of powerful treasure and the Jupiter Djinni Gale, is the battle with the powerful and tricky optional boss Star Magician, and defeating it earns you the Azul summon sequence.

Yampi Desert Cave
Yampi Desert Cave, hidden within the early-game area of Yampi Desert and accessible only with the Teleport Psynergy, is one of the four main optional late-game dungeons. It is large and inter-connected, and is home to the Venus Djinni Crystal. At the end is the battle with the burly boss Valukar, and defeating it earns you the Daedalus summon seqeuence.

Islet Cave
Islet Cave, accessible with the turtle at the Sea of Time Islet only after completing a chain of trades across the Great Eastern Sea, has an area that can be accessed much earlier and gives you the Venus Djinni Meld. With the Teleport Psynergy, you gain access to a very straightforward series of halls, one of which contains the Mercury Djinni Serac, and at the end is the battle with the powerful boss Sentinel. Defeating it earns you the Catastrophe summon sequence.

Anemos Inner Sanctum
Anemos Inner Sanctum is the interior portion of Anemos Sanctum that can only be accessed by both the Teleport Psynergy and by collecting all 72 Djinn in the Golden Sun series. It is the intended ultimate challenge of the game, and contains both of the heaviest summons in the game, Charon and Iris. At the end is the battle with the strongest optional boss in the series, Dullahan, which you must fight for Iris.

Trivia
An interesting thing about the four main optional dungeons in The Lost Age is that three of them, Treasure Island, Islet Cave, and Yampi Desert Cave, represent a specific element, Mercury, Jupiter, and Mars respectively, as said by their bosses, with Anemos Inner Sanctum representing light, as said by Dullahan. Venus is oddly missing from this supposed pattern. There is a slight amount of speculation that the Parchable lake in Mikasalla was meant to lead to this dungeon, but was scrapped by Camelot. Another theory is that the dungeon Lunpa claimed to get the Grind Stone from was meant to represent this, with the programers not putting the dungeon into the gamecode for some reason. However, the Dullahan itself is heavily Venus-based in its resistances, and it is likely just fan speculation, especially considering connections between Light and Earth made elsewhere in the game.