EQ Might includes a wide selection of standard and custom large bags, available through exploration in multiple zones or via purchase with specific currencies. Below is a list of most of the bags you can obtain.
non-exhaustive list
Bag of the Tinkerers (lore)
weight 1.0, bag size: giant, weight reduction: 100%
sold by Nacho in the Plane of Knowledge
Box of Abu-Kar (No Trade, lore)
weight 2.0, bag size: giant, weight reduction: 100%
dropped in Nagafen's Lair and Permafrost
Box of Nil Space (lore)
weight 5.0, bag size: giant, weight reduction: 70%
dropped by Harbringer Freglor in Sebilis
Hynid-Hide Backpack
weight 3.5, bag size: medium, weight reduction: 30%
sold by Gene in the Plane of Knowledge
Kavruul`s Mystic Pouch
weight 0.4, bag size: giant, weight reduction: 100%
dropped by various dragons, including Lady Vox and Lord Nagafen
Leafbound Trailbag (lore)
weight 0.5, bag size: giant, weight reduction: 50%
starter bag, sold by Walter in the Plane of Knowledge
Stoneweft Trailbag (lore)
weight 2.0, bag size: giant, weight reduction: 50%
global random drop of level 10-44 NPCs
Treasure Hunter's Satchel
weight 1.0, bag size: giant, weight reduction: 100%
dropped by various dragons, including Lady Vox and Lord Nagafen
Bag of the Young Warden (No Trade, lore)
weight 0.4, bag size: giant, weight reduction: 100%
dropped by The Pathless Sentinel in The Grey (warden instance)
Very Large Coin Purse (No Trade, lore)
weight 0.1, bag size: large, weight reduction: 70%
dropped by Lord Yelinak in Skyshrine
Wyvern Skin Bag (No Trade, lore)
weight 0.4, bag size: giant, weight reduction: 90%
dropped by Ragnoor the Defender in Veeshan's Peak
Braided Horsehair Handbag (No Trade, lore)
weight 0.1, bag size: giant, weight reduction: 90%
crafted with tailoring (no-fail, requires 1x Fur of Taskmistress Krisz, 4x Pristine Ixt Fur)
Fabled Box of Abu-Kar (No Trade, lore)
weight 0.2, bag size: giant, weight reduction: 100%
dropped by The Fabled Nerioth in Fabled Nagafen's Lair
Fabled Treasure Hunter's Satchel
weight 0.4, bag size: giant, weight reduction: 100%
dropped by Legendary Treasure Chest of Fabled Nagafen in Fabled Nagafen's Lair
Frizznik's Endless Coin Purse
weight 0.1, bag size: giant, weight reduction: 90%
reward from Aid Eido's quest "Essences of Power"
Scalekit
weight 0.6, bag size: giant, weight reduction: 90%
dropped by Tirannun in Tirranun's Delve
White Dragon Leather Bag (No Trade, lore)
weight 0.4, bag size: giant, weight reduction: 100%
dropped by Legendary Treasure Chest of Fabled Lady Vox in Fabled Permafrost (duo instance)
Ice Silk Bag (No Trade, lore)
weight 0.6, bag size: giant, weight reduction: 100%
dropped by Legendary Treasure Chest of Voras the Spider Matriarch in The Spider Den
Venomette (No Trade, lore)
weight 0.3, bag size: giant, weight reduction: 100%
dropped by Legendary Treasure Chest of Vipera in Anguish
Zordak's Masterbox (No Trade, lore)
weight 0.2, bag size: giant, weight reduction: 100%
dropped by Legendary Treasure Chest of Zordakin in Fabled Nagafen's Lair (intense mode)
Bulging Knapsack
weight 7.5, bag size: large, weight reduction: 10%
sold by Marcus in Plane of Knowledge for Tokens of Legendary Might
Epic Black Bag
weight 0.7, bag size: large, weight reduction: 100%
rare random drop of various high level treasure chests and NPCs
Kirin Leather Backpack (No Trade, lore)
weight 0.5, bag size: giant, weight reduction: 100%
dropped by Icehoof and Treasure Chest of Thornheart in Stillmoon (duo instance)
sold by Tamara the Dragontamer in Plane of Knowledge
Legendary Traveler's Pouch (No Trade)
weight 0.4, bag size: giant, weight reduction: 100%
sold by Marcus in Plane of Knowledge for Tokens of Legendary Might
Noble Leather Pouch (No Trade, lore)
weight 0.3, bag size: giant, weight reduction: 100%
dropped by Trysta the Dark Tutor and Madame Chiasa in Chambers of Eternal Affliction
Second Breakfast Sack (Lore)
weight 0.5, bag size: giant, weight reduction: 95%
sold by Selina Selia in The Temple of Marr in Freeport for Platinum
Summoran's Rune-Etched Box (No Trade, lore)
weight 0.2, bag size: giant, weight reduction: 100%
dropped by Legendary Treasure Chest of Summoran in Bloodied Quarries
Lion Leather Backpack (No Trade, lore)
weight 0.5, bag size: giant, weight reduction: 100%
dropped by Solstice the Firemane in Stillmoon (duo instance)
sold by Tamara the Dragontamer in Plane of Knowledge for Stillmoon Reliquaries
Red Dragonhide Carryall (No Trade, lore)
weight 0.1, bag size: giant, weight reduction: 100%
dropped by Lord Infernon in the Fabled Plane of Fire
sold by Rick Magmo in Plane of Knowledge
Surefall Glades Pouch
weight 0.5, bag size: giant, weight reduction: 100%
Dust of Might reward from Dustin Surefall in Surefall Glades
Timeless Bag of Sewn Evil-Eye (No Trade, lore)
weight 3.0, bag size: giant, weight reduction: 100%
dropped by Timeless Evil Eye in Timeless Lower Guk (trio instance)
Wyrmscale Carryall (No Trade, lore)
weight 0.2, bag size: giant, weight reduction: 100%
dropped by Mistress Mistrilla in Timeless Western Wastes
sold by Javier in the Plane of Knowledge
Bag of Dark Secrets (No Trade, lore)
weight 0.2, bag size: giant, weight reduction: 100%
dropped by Nerro in Veeshan's Peak 3.0
Legendary Lion Leather Backpack (No Trade, lore)
weight 0.4, bag size: giant, weight reduction: 100%
dropped by Treasure Chest of Solstice in Stillmoon (duo instance)
Legendary Red Dragonhide Carryall (No Trade, lore)
weight 0.1, bag size: giant, weight reduction: 100%
dropped by Lord Infernon in the Fabled Plane of Fire
Legendary Wyrmscale Carryall (No Trade, lore)
weight 0.2, bag size: giant, weight reduction: 100%
dropped by Mistress Mistrilla in Timeless Western Wastes
sold by Javier in the Plane of Knowledge
Dragon Treasure Chest (No Trade, lore)
weight 0.2, bag size: giant, weight reduction: 100%
dropped by Skaramatra the Risen in the Lair of the Risen and Nerro in Veeshan's Peak 3.0
Harmonic Case (No Trade, lore)
weight 0.5, bag size: giant, weight reduction: 100%
dropped by The Silent Pianist in Chambers of Eternal Affliction (intense mode)
Heavy Iron Container
weight 275, bag size: giant
sold by Gene McGoodman in Plane of Knowledge for Platinum
Mythical Bag of Surefall (No Trade)
weight 0.3, bag size: giant, weight reduction: 100%
Dust of Might reward from Dustin Surefall in Surefall Glades
3rd Anniversary Box (No Trade)
weight 0.5, bag size: giant, weight reduction: 100%
random drop, mostly during the 3rd anniversary period, very rare drop afterwards