Gearing up at Endgame

[Rustle Mint]

ilvl 55
Wanderer's Palace (Normal Mode) - Drops left-side gear, last boss drops weapons.
Amdapor Keep (Normal Mode) - Drops left-side gear, last boss drops weapons.
These two dungeons have no ilvl requirement to queue.

ilvl 60
Pharos Sirius - Left-side gear and accessories. (Requires ilvl 48 to queue)
Copperbell Mines (Hard Mode) - Left-side gear and accessories. (Requires ilvl 48 to queue)
Haukke Manor (Hard Mode) - Left-side gear and accessories. (Requires ilvl 48 to queue)
Ifrit Hard Mode - Weapons

ilvl 70 (AKA Darklight Gear)
Lost City of Amdapor - Left-side gear and accessories (Requires ilvl 55 to queue)
Halatali (Hard Mode) - Left-side gear and accessories (Requires ilvl 55 to queue)
Brayflox's Longstop (Hard Mode) - Left-side gear and accessories (Requires ilvl 55 to queue)
Garuda Hard Mode - Weapons

ilvl 75
Thormarch (Hard) - Weapons (Requires ilvl 54 to queue)

ilvl 80
Hullbreaker Isle - Left-side gear and accessories (Requires ilvl 70 to queue)
Tam-Tara Deepcroft (Hard Mode) - Left-side gear and accessories (Requires ilvl 70 to queue)
Stone Vigil (Hard Mode) - Left-side gear and accessories (Requires ilvl 70 to queue)
Crystal Tower Wing 1 (Labyrinth of the Ancients) - Left-side gear (Requires ilvl 50 to queue)
Ultima Weapon (Hard Mode) - Necklaces and Rings
Titan Hard Mode - Weapons
Basic Relic Weapon

ilvl 90
Snowcloak* - Accessories (Requires ilvl 80 to queue, and progression through story quest)
Sastasha (Hard)* - Accessories (Requires ilvl 80 to queue)
Sunken Temple of Qarn (Hard)* - Accessories (Requires ilvl 80 to queue)
* These dungeons drop Antique items which can be exchanged for ilvl 90 left-side gear in Mor Dhona.

Garuda Extreme - Rings (Requires ilvl65 to queue)
Titan Extreme - Earrings (Requires ilvl67 to queue)
Ifrit Extreme - Bracelet (Requires ilvl70 to queue)
"Primal Weapons" - Completing the weekly Quest "Primal Focus" (requires a kill of Garuda, Titan and Ifrit Extreme) gives tokens that can be turned in for a weapon.
Binding Coil of Bahamut, turns 1-5 - Left-side gear and accessories. (Requires between 70 and 82 average ilvl to queue, depending on the turn)
Relic Weapon Zenith

ilvl 95
Leviathan Extreme - Weapons (Requires ilvl 80 to queue)
Binding Coil of Bahamut, turn 5 - Weapons (Requires ilvl 80 to queue)

ilvl 100
Keeper of the Lake - Left-side gear and accessories (Requires ilvl 90 to queue, and progression through story quest)
Wanderer's Palace (Hard Mode) - Left-side gear and accessories (Requires ilvl 90 to queue)
Amdapor Keep (Hard Mode) - Left-side gear and accessories (Requires ilvl 90 to queue)
Crystal Tower Wing 2 (Syrcus Tower) - Left-side gear (Requires ilvl 70 to queue)
Soldiery Gear - Left-side gear, accessories
Soldiery Weapons - Turn in at Mor Dhona: 10 Rowena's Token (Soldiery) + 1 Unidentified Allagan Tomestone
Tokens are purchased for Soldiery at 130 each
Unidentified Allagan Tomestones are won in wing 2 of Crystal Tower
These weapons can be upgraded to ilvl 110 with Sands of Time from wing 2 of Crystal Tower
Mog Extreme - Necklaces (Requires ilvl 80 to queue)
Ramuh Extreme - Rings and Weapons (Requires ilvl 85 to queue)
Upgraded Leviathan Weapons - Must obtain weapon from Leviathan as well as a Mirror of the Whorl which also drops from Leviathan.Good luck on those rolls!
Relic Weapon Atma
Relic Weapon Animus

ilvl110
Upgraded Soldiery Gear/Weapons - You can turn in soldiery gear and Oil of Time (accessories) or Sands of Time (left-side gear/weapons) at Hyrstmill.
Oil of TIme and Sands of Time are won in wing 2 of Crystal Tower
Shiva Extreme - Weapons (requires ilvl 95 to queue) (These weapons can be upgraded to i115)
Second Coil of Bahamut. Turn 6-9 - Left-side gear and accessories.
Relic Weapon Novus

ilvl 115
Upgrade Shiva Weapons - Must win shiva weapon and 5 diamond dust (for paladin: 3 for weapon, 2 for shield). Turn in at Mor Dhona
Second Coil of Bahamut, Turn 9 - Weapons
Relic Weapon Nexus

ilvl 120
Crystal Tower Wing 3 (World of Darkness) - Left-side Gear (Requires ilvl 90 to queue)
NOTE: In World of Darkness, you can only win ONE loot item per week. If you win something on a greed roll, it counts, so don't roll unless you mean it! Resets each week on Tuesday.
Shiva Extreme - Bracelets
Poetics Gear - Left side gear and accessories
Ironworks Weapons - Get Encrypted Tomestone from CT weekly, you can turn it in (along with 10 poetics tokens - 130 poetics each)for an i120 weapon. This can be upgraded to 130 at Hyrstmill with a Carbontwine (another reward from weekly, or can turn in Unstained Mark Logs. 6 logs -> 1 carbontwine).

ilvl 125
Zodiac Weapon

ilvl130
Upgraded Poetics Gear - You can upgrade your gear to 130 with Carboncoat (accessories) or Carbontwine (left-side gear).
Carboncoat is obtained from the Coil, weekly Crystal Tower quest, or you can buy Unstained Mark Logs for Allied Seals to turn in. 4 logs -> 1 carboncoat
Carbontwine is obtained from Coil, weekly Crystal Tower quest, or you can buy Unstained Mark Logs for Allied Seals to turn in. 6 logs -> 1 carbontwine. As of 2.5, you can get Carbontwine from CT weekly as well!
Each Unstained Mark Log costs 500 Allied Seals (which are obtained from Hunts)
Final Coil of Bahamut, Turn 9-13 - Left-side gear and accessories

ilvl 135
Final Coil of Bahamut, Turn 13 - Weapons
Zodiac Weapon Zeta (final step for relic weapon before expansion)