Reforge

Reforging is a means of randomizing the additional mods to a base item. The Goblin Tinkerer charges money for this process, and it is applied once for free when an item that can have additional mods is encountered for the first time. This process generates stats that are broadly useful, such as movement speed or increased defense, for as long as the item is equipped. As the mods are randomized, it is possible to get stats on items that give up to 5 bonuses at once or with bad luck 3 stats are lowerd up to 25%. The amount depends on the items base values which are multiplied with a fixed value and then rounded. So one item can get +15% damage i.e. while an other items with the same modification gets +16%.

The process is expensive, and is probably intended as a "gold sink." If the item is crafted, one means of generating new mods is to rebuild the item; that may not be practical, hence the "Reforge" option on the Tinkerer. Currently, the Goblin Tinkerer charges the items sell value * 5 (reforged items are more expensive to reforge again due to their higher sell value).

Not all items seem to be acceptable to modify, despite their category. Tomes of Water Bolt cannot be reforged, but Flower of Fire can, so some spell weapons are not able to be benefited in this way.

It should be noted that an item with mods can be used in the crafting of other items if it is marked as a material. Doing so does not preserve the mods; an Enchanted Boomerang's mods are lost when used to create a Flamarang, which will get new mods randomly assigned upon creation. Thus, if you have a weapon or accessory that already has useful mods, you may wish to consider finding another of the same to use in crafting.

There are 83 different reforge modifications in total at the moment (19 accessory + 64 weapon).

Accessory Mods
Accessory mods are always "on" -- they are applied to the character no matter what they are wielding, as long as they are equipped. Every accessory item can be reforged with the exception of Guide Voodoo Doll and all Music Boxes. Accessories can have one of the following mods attached to them:

Weapon mods
These mods only apply when the weapon is being used.

Universal
Flails, Spears, Boomerangs and Chainsaws can only be reforged with these mods. These mods can also be used by any weapon in the game. The best mod for those items is Godly. Drills can only be reforged with mods that don't change Knockback.

Common
All weapons that are either melee, ranged, or magical can have these mods. There is no weapon whose best mod is in this category, though these mods are not especially bad.

Melee
All Pickaxes, Hammers, Hamaxe and Melee Weapons can be reforged with these mods, in addition to the top two categories. The best melee prefix is Legendary.

Ranged
All Bows, Repeaters and Guns (Excluding the Space Gun and Laser Rifle which count as Magic Weapon) can be reforged with one of the following mods, in addition to the top two categories. The best ranged prefix is Unreal.

Magic
All Magic Weapons (mana consuming) with the exception of the Water Bolt can be reforged with one of the following mods, in addition to the top two categories. The best magic prefix is Mythical.

Complete List
Less the Attack Animation Speed the better. Less the Mana Cost the better.