Here is the list of all skills, discovered by trial and error, and their descriptions.

There are a total of three skill slots on a character regardless of anything you may think. There are 100×100 = 10,000 possible combinations of Weapon/Armor, 100×185 = 18,500 possible combinations of Weapon/Pet and Armor/Pet. That means that there is a staggering 1,850,000 (that's over 1.8 million) combinations of Weapon/Armor/Pet. Despite this very large number, not all combinations yield a skill. Some items yield a skill regardless of other equipment in some cases, for example the Dice, Golddice and Nitedice which all yield the skill Chance.

Some Skills are cumulative (Recovery5 + Recovery10 = 15HP/Second) whereas others are multiplicative such as Powup and No Guard, (Powup 20+ Powup 30 = Pow*120%*130%= Pow*156% = Powup 56). 

Weapons/Armour combinations can be found here .

Pet/Weapon combinations can be found here .

Pet/Armour combinations can be found here .

A Three Skill Set or List of Builds can be found here .

A list of all equipment that produces a set skill can be found here.

A google spreadsheet that everybody can contribute to here (managed by user:happypal).

A Skill calculator can be found here. The set data is extracted from /u/soulctcher's spreadsheet and the distance data is from theMinuteQuest Wikia.

Skill Name Description
Absorption Each time the Hero gives damage, you recover "Damage/100", does not exceed remaining HP of the monster.
Acc Up Increase Accuracy by x%. (Max 50)
Acrobat Speed raises damage. 
Analysis Increase Accuracy.
Arm Twister Pow raises Evasion.
Avoid Risk Repel brutal monsters by 90%. (Doesn't apply in Dungeons)
Bide You need one less hit to kill. Which means you kill a monster directly if it's Hp is is less than 2x your actual Damage.
Big Defense Your movespeed becomes very slow but the damage you receive is divided by two.
Body Slam Vit raises Damage. (How much ?) Speculation: Vit/3 + Base Damage
Brat Kings spoils you. (2 golds per coin received hitting "Pay Up!")
Chance The damage you deal depends upon your Luck stat.
Counter Sometimes gives a hit back to a monster.
Crit Up Critical Hit probability increased by x%. (Max 50)
Cursed Take damage when you attack, however attacks are slightly stronger.(Exact value unknown)
Dash Move speed is fixed and fast. (Ignore Weight)
Death March The hero goes in the direction pointed by himself.(Automatic run)
Demon Dash Move speed is fixed (Ignore Weight). Your Hero goes faster than SuperDash.
Devil Luck Luck increases Evasion.
Discovery OreKing, Mimic and Dr.Gill have better chance to appear.
Early Bird Stronger at morning.
Elem Up Increase Elemental damage by x%. (Max 50)
Exp Farmer Double your Exp reward but you don't get any Gold.
Exp Up Boost your Exp reward by x%. (Max 50)
Feng Shui Int increases Luck.
Gold Digger Double your Gold reward but Exp reward is reduced to 1/3.
Gold Up Boost your Gold reward by x%. (Max 50)
Grounded When a monster touches you, you aren't bumped backward and you still continue to attack.
Guard Up More resistant to hits by x%. (Max 50)
Guts Fight until the end. (leaves you with 1hp before you die)
Healer Each time you attack, you gain the Hp you earn by your recovery stat.
Jammy Luck raises Accuracy and Damage. 
Killer Have a chance to kill a monster in one hit. Doesn't affect Boss.
Luck Up Boost your Luck. (Around *1.5)
Lucky Received damage is random and depends of your Luck.
Mach Hit Faster Auto-Attack. (Around *1.5 faster or fixed)
Madman Boost hit rate by 1.5 but reduce damage done by 50%.
Magiwall Reduce Magic damage by 50%.
Magic Hit Int become the stat used for damage calculation instead of Pow.
MGuard Up More resistant to Magic by x%. (Max 50)
Night Owl Stronger at night.
No Guard Boost damage done by 50% but damage taken is double.
Paralyse Sometimes (1/5 estimate) when you hit a foes, he becomes paralyzed and doesn't attack for 3sec.
Pet Up Increase the Attack speed of your pet by x%. (Max 50)
Poison Induces a status on the monster that deals damage through time.
Power Up Power Up X : Increase Power by X% (Max 50). Be careful, damage isn't increased by X%. (Need to find damage formula)
Provoke Five monsters will always appear in frames outside of dungeons
Rage Power up near death
Retaliate Never miss a Counter. (You need the Counter skill for this to apply)
Recovery Your Hp regen become "x" instead of 1. (Max 10)
Reflect Counter all attacks.
Scapegoat When your Hp comes to 0, your pet die instead of you and you recover your Hp by half.
Slow Hit Hits enemies slowly.
Speed Up Increase your Evasion by x%. (Max 50)
Spell Powerful first hit.
Stinky Monsters appears more rarely.
Super Mach Faster Auto-Attack. (Around *2 and *3)
Surprise The first hit is always successful.
Treasure Up Increase treasures drops by x%. (Max 30)
Unfair Accuracy increased by a lot. (100% boost estimate)
Wall Reduce Physical damage by 50%.
Warper When the hero comes close to a monster, he's teleported directly on it. You always touch the monster at least one time before his first attack.
Weakness Up Stronger against monsters weakness.
Vigilance Monster can't attack first.