Epics are purple-named items which are very rare. Most have huge potential to be the best of their kind. Finding an epic is all about luck, you could find it on first kill, or go weeks without finding one, so take it easy and just farm away, sooner or later it will happen.
Also some epics can be seen equipped on the monster portrait, but it's a gamble as it's not 100%, so it isn't worth running from monsters until you see one as you might skip an epic.
Now to each epic and the most effective methods to farm them, ordered by how dangerous each is to farm and with a score of how good they are:
Bear Hands - 1/10
Description: Bear hands are simply a cosmetic epic, no real use to it.
Drops from: Bear
Best spots to farm: Wildeburn Forest
Strategy: Just kill bears until you find one. Gear is whatever you have at the moment.
Suffering's End - 10/10
Description: Best gloves in the game, can roll insanely well and is probably the second most rare epic in the game, but it's really easy to mindlessly farm Kobolds which are harmless and can be farmed for good battleaxes on top of the epic.
Best spots to farm: Kobold Settlement
Strategy: Kill kobold after kobold on an endless farm. Gear doesn't matter much.
Fate's Call - 3/10
Description: Ok pierce weapon, can roll 100+ max damage but most of the times is a subpar high dura rapier.
Drops from: Skeletal Scout
Strategy: Can be farmed along Monstrous Orc Shaman on temple ruins areas or with skeletal duelists for rapiers on castle grounds. Use piercing block armor if farming for rapiers, and bludgeoning armor if farming for shaman.
Can also be side farmed along with crusader (scroll down).
Final Favor - 10/10
Description: Best shield in the game and possibly best epic all around, even the worst roll possible is very good.
Drops from: Lunar Magistrate
Best spots to farm: Aphelion Shrine
Strategy: Run from all mobs except magistrates, or kill lunar guards to get scales while at it. Magistrates drops plates and large chests which is a bonus. The area is quite harmless so basic gear works.
Thorn - 8/10
Description: Most famous epic probably and one of the oldest, thorn is very good due to bonus dex, mixed damage and also the possibility for very high rolls such as 4d8 x4.
Strategy: Use any decent piercing armor to avoid the annoying crits from regular daggers, farm the spots to none in the order listed above, once finished head back to first one. You can spam create camps to force spawn mobs which makes things quite fast. Incidentally, you will earn a lot of gold whilst farming this.
Wrath of Lotan - 3/10
Description: Hit or miss, can be as low as 20 max damage or 100+, due to being a 2-handed weapon, it isn't used on end-game content as 1 handed weapons can do better work.
Drops from: Merman
Strategy: Just skip all murlocs and crabs and focus on Mermen. Can be farmed along with Collosal Crustacian possibly for decent shields, not many players farm for these, except to check it out of the list.
Fury of Xolotl - 4/10
Description: If you thought most epics were hard to get, you forgot to get this one. Overall, it is just a purple Macuahuitl that can roll significantly better. With a low dex pen, bludgeoning/piercing damage types, and one handed wielding, it is a very nice epic overall.
Drops from: Acolyte
Best spots to farm: Temple Ruins
Strategy: If you decide to acquire a Macuahuitl collection, this is a nice great epic to happen upon. Temple Ruins are where Acolytes spawn, leaving you with one good place to power-farm for this. This is a weapon that drops in an area where you go when farming for the non-epic version of this weapon, meaning that you are already geared for this to drop.
The Really Greatclub - 2/10
Description: Decent club used for farming or nothing, simple as that. Often abbreviated to 'RGC'.
Strategy: Use bludgeoning blocking gear such as plate to avoid the high strength hits. Giant ogres possibly have higher drop rate of it.
Hailstorm - 1/10
Description: Pretty average epic on the worst spot possible to farm the worst monster in the game. Not worth the time at all as GKA (Grave Kings Axe) is much better alternative on a decent farm spot.
Drops from: Frost Giant
Best spots to farm: Grand Mountain Summit is the only spot.
Strategy: Just kill giant after giant, they use slash so bring a plate of sorts, takes 10+ explores to find a single giant, and the area can't hold many, and it's also a slow respawn, so this is the worst combination possible.
Grace of Il'Kalet - 9/10
Description: Best helmet only beaten by a good roll Protector's helm. Only piece of armor to effectively block the bludge/pierce combo, making it awesome to fight Elf with.
Drops from: Lizard Soldier
Best spots to farm: Lizardfolk Marshland on any area with good monster activity.
Strategy: Just skip the lizard hunters and stick to soldiers only. Lots of gold to be made here and Lizard King can be found for good sword/bracers/helm. One of the best epics to farm in general.
The Black Blade - 2/10
Description: Average Emerald Sword but purple, also way rarer than it should be, so odds of finding one are probably the worst.
Drops from: Black Guard in general, the stronger the better for odds.
Best spots to farm: Black Mountain
Strategy: Black mountain spamming camps, use macuas and full-plate and just farm, be aware the chances are close to none and the epic is totally not worth it except for being way too rare.
Python Scale Tunic - 10/10
Description: The best shirt in the game, no matter the roll, quite easy to farm but a bit boring, upside of it is the ability to stock up on snake shirts.
Drops from: Desert Python
Best spots to farm: Serpent Pit
Strategy: Use nomad plates and swords to farm them, the snakes deal bludge/pierce, and a camp can be made outside the pit, quite straight forward farming.
Gungnir - 4/10
Description: Fancy half-pike, a good bonus on top of farming for gold, the best overall 2-handed piercing epic, with good block, damage, and an additional damage type.
Drops from: Dragon Hunter
Strategy: Dragon hunters are quite rare, the spawn rate is probably better at cinder area, but it's much more unforgiving. Charred is preferred for being safer, closer to Aera and a good gold farming spot.
Use piercing block gear and a bludge weapon + heavy steel shield. Don't underestimate the dragon hunters.
Malediction, Herald of Pain - 6/10
Description: A great epic due to its bludgeoning/piercing dual damage type and a/a/a blocking. However, it is rather similar to Forgive and Forget in that it is a two handed weapon with a comparably poor block chance, leaving players with many better options for weapons with the amount of times it takes to get this rare epic.
Drops from: Hobgoblin Hunter
Strategy: If all you care about is the epic, then the Hobgoblin Tribe Campsite is your best bet. However, they also can drop anywhere along the Cliffside Lookout trail, meaning that you can also farm for the Protector of the Plains while you look for this epic.
Seven-League Boots - 8/10
Description: After the boots rebalancing, these are the best dex-wise, getting a top 3 spot on boots in the game.
Drops from: Aseridith Squire
Best spots to farm: Good spawns not confirmed yet, but Aseridith area spawns squires.
Retribution - 7/10
Description: Usually rolls close to a high roll warhammer, but with massive dura, it's a quite good epic considering the area would be farmed even without it there.
Drops from: Orc Captain
Strategy: Farm for orc captains only, skip all other mobs, do it on climb until its activity is none, then move to forest while climb fills back up. Orc captains, wield weapons of all 3 damage types, and they hit hard so farming with 2 alts is recommended, one with full-plate will fight warhammers and axes and the scales for crossbow. Nomad plates also works very well, even better than scales but harder to find.
Healing can be done 2 areas further from climb, at the lake.
Grave King's Axe - 8/10
Description: The best 2-handed epic, has mixed high damage and is an improved version of one of the best weapons/2-handed in the game, the Groundkeepers Axe.
Drops from: Cemetery Groundskeeper
Best spots to farm: Inside crypts has better odds, but otherwise all around the cemetery.
Strategy: Drops from a rare spawn, so it's very boring, on the bright side, GK axes are amazing as weapon so the farm isn't worthless. Inside crypts there are better spawn rate but the risk of stumbling upon AoD.
Groundskeeper deal very high crits, so gear properly with full plate and good items against both bludgeoning and slashing.
Forgive and Forget - 3/10
Description: The epic looks and is really cool, but not much can be said as useful as it is a 2-handed that doesn't beat 1-handed on damage or shields on block. It's also very hard to farm because it drops from a rare spawn on a very deadly area.
Drops from: Desert Assassin
Best spots to farm: Rolling Dunes before nomad camp and nomad area.
Strategy: Very high piercing and slashing block armor to absorb the shurikens and blades in the area, the assassins are a very rare spawn so just use same strategy as for finding magistrates, skip anything not wanted.
Molten Blade - 5/10
Description: The best sword or slashing epic available, it consistently rolls 54+ max damage and can give bonus dexterity, durability is also quite good.
Drops from: Fire Elemental
Best spots to farm: Core of Smoldering Mountain
Strategy: Kill elemental after elemental to find it, the fire crystals might have some use later on and some players also collect them. Very boring to farm and deadly as elementals deal high piercing criticals from time to time.
Crusader - 10/10
Description: Best all around armor seconded to pre-nerf prots, but with 3k+ dura, the shiniest art and also the rarest epic, crusader is highly sought but only few people have it.
Drops from: Skeletal Commander
Best spots to farm: Deathly Forest
Strategy: Skeletal commanders have very high dexterity, hp, strength, living up to the name of where they "live". Slash blocking gear at all times, pierce is needed. Macuas shield combo works nicely, or 2-handed pierce can be used to avoid the low dura hassle.
Same area is home to skeletal scouts, which drop fates call (scroll up).