How does this question differ from What items are worth picking up? That question is more about what items are worth keeping between home-runs, so to speak. My question is more about longer term storage and selling.
In Path of Exile, there's no gold (piece) economy. It is based on currency items which each have their own use and their prices are relative. It's a barter economy. The other integral half of the economy is combat items: weapons, armour, jewelry, maps, and skill gems.
Among what determines a weapon's or armour's worth are: sockets, links, item-level, and the mods that are on it. I want to focus on the mods. There are two types of mods, implicit and affixes. Implicit mods always come with a certain weapon type. The more important type of mod are affixes.
Mundane (non-magic) items are items without affixes. Affixes are split into two categories: prefixes or suffixes. A magic (indigo) item can have up to one prefix and suffix. More than that and it becomes a rare (yellow) item.
Now, you may say that what determines an item's worth is the mods that you're looking for, which can vary greatly. I believe that it doesn't vary greatly. While the mods that are desired differ based on build, there are certain sets of mods that are desired on each individual item (weapon, jewelry, and armour pieces (chest, helmet, gloves, and boots)). The most-easily-notable universally-desired sets are Increased Item Rarity + Increased Item Quantity (A.K.A. "Magic Find") and elemental resistances + increased armour/evasion/energy shield. I could name maybe a few more, but I'll leave the rest to the answerer.
What determines whether an item is worth selling on the market, vending to an NPC, or auctioning (particularly, in terms of mods/affixes)?
Best Answer
tl;dr: Items that people want to have are expensive, other items are not. I suggest using a service like poe.xyz.is to get a feeling for the value of an item you might want to sell. Especially for uniques it can give you a very good idea of an item's value.
This is a pretty open-ended question so a conclusive answer may be hard to come by. That said...
Affixes come in different brackets, or tiers. For example, % Increased Physical Damage comes in 7 tiers ranging from "Heavy" (+20..49% IPD) to "Tyrannical" (+150..169% IPD). The stronger brackets are of course more valuable, while the weaker ones may even reduce the value of an items since they prevent stronger ones from spawning.
Movement speed is incredibly important on boots since it cannot spawn on other gear, and it's rare to see a pair without MS sell at all, let alone fetching a high price.
Affixes that align well with the base item type are more expensive. E.g. Increased Critical Strike Chance is much better on a Dagger than it is on a Maul, because Daggers already have a high base crit chance and are therefore commonly used in crit builds, while Mauls are strength-aligned and often used by characters who cannot crit due to Resolute Technique.
Affixes that align well with each other can increase the value of an item - or rather, affixes that don't align can relegate an item to the vendors. A combination like % Increased Physical Damage and flat Increased Physical Damage, or +2 to Fire gems and +1 to all gems can get quite expensive, while no build I know of makes good use of both Attack Speed and Cast Speed. Especially on base types with a large mod pool (e.g. jewellery, daggers, wands, sceptres, staves) having well-aligned affixes can increase the value dramatically.
Resistances are pretty popular on socket-less items because they're easier to swap around to accommodate changes in your other gear.
With the release of Forsaken Masters, a 5-affix item may well be more valuable than that same item with a 'decent' 6th affix, because it leaves some room for the buyer to customize the item.
Corrupted items are in general less valuable than their non-corrupted variants because the sockets are locked, but if they rolled a very good corruption this is of course not the case.
It could be said that different factors have multiplicative scaling - e.g. a 6L item is expensive, and an item with good affixes is expensive, but a 6L item with good affixes will not simply be twice as expensive - it will cost you three and a half fortunes.