These may be needed for gearing, unlocking roulettes, or just progression that are not related to the main scenario.

Side Note: You must have finished the Main Scenario as of 2.0 to get these quests (Final 2.0 Quest: The Ultimate Weapon).

The Weaponsmith of Legend - Unlocks relic weapon quest chain. Quest given at Western Thanalan (11,14).

A Self-improving Man - Unlocks glamour system. Quest given at Mor Dhona (22,6).

Like Civilized Men and Women - Unlocks Frontlines PvP. Requires A Pup No Longer to be complete. Quest given at your GC.

Let the Hunt Begin - Unlocks daily (random mobs and notorious monster FATEs) and weekly (B-rank) hunt marks. Quest given at your GC.

Of Errant Epistles - Unlocks the Delivery Moogle Quests. Quest given at Mor Dhona (30,13).

The Rise and Fall of Gentlemen - Unlocks the Hildibrand Side Quest. Quest given at Ul'dah the Steps of Nald (9,8).

A Recurring Problem - Unlocks the Primal HM chain (ie. Ifrit HM (iLvl 49), Garuda HM (iLvl 52), and Titan HM (iLvl 57)). Quest given at the Waking Sands in Western Thanalan (6,6).

Trauma Queen - Unlocks Wanderer's Palace (No item level requirement). Quest given at Western Thanalan (11,13).

Ghosts of Amdapor - Unlocks Amdapor Keep (No item level requirement). Quest given at Western Thanalan (12,14).

Sirius Business - Unlocks Pharos Sirius (iLvl 48). Quest given at Western La Noscea in Aleport (26,26).

Maniac Manor - Unlocks Haukke Manor HM (iLvl 48). Quest given at Mor Dhona (22,8).

Out of Sight, Out of Mine - Unlocks Copperbell Mines HM (iLvl 48). Quest given at Mor Dhona (22,8).

One Night in Amdapor - Unlocks Lost City of Amdapor (iLvl 55). Quest given at Old Gridania (6,10).

This Time's for Fun - Unlocks Halatali HM (iLvl 55). Quest given at Mor Dhona (22,8).

Curds and Slay - Unlocks Brayflox's Longstop HM (iLvl 55). Quest given at Mor Dhona (22,8).

King of the Hull - Unlocks Hullbreaker Isle (iLvl 70). Quest given at Mor Dhona (22,8).

Blood for Stone - Unlocks Stone Vigil HM (iLvl 70). Quest given at Mor Dhona (21,8).

Corpse Groom - Unlocks Tam-Tara Deepcroft HM (iLvl 70). Quest given at Ul'dah the Steps of Nald (12, 8)

It's Definitely Pirates - Unlocks Sastasha HM (iLvl 80). Quest given at Mor Dhona (22,8).

The Wrath of Qarn - The Sunken Temple of Qarn HM (iLvl 80). Quest given at Mor Dhona (22,8).