A Fantastic Treasure
This page lists a number of example Items you might want to consider using as a core for your homebrew build. This is not even close to an exhaustive list, but it does try to give some representative examples of the things that are possible in Path of Exile and how builds can differ from one another.
The Dancing Dervish / The Dancing Duo
Take your partner by the hand, / Keep your steps in time. / Swing together, spin apart, / And dance with death sublime.
The Dancing Dervish, and its upgraded version the Dancing Duo, is a Unique two-handed sword. It gives you the Rampage effect, which triggers when you kill many enemies in rapid succession. As soon as your Rampage triggers, the sword becomes an independent minion and fights for you autonomously, leaving you without a weapon for as long as you can maintain your kill streak. Since the sword-animation skill is triggered by the sword itself, it benefits from any Support gem socketed in the item regardless of links (as is usually the case for a skill innate to an item). For example, a Minion Damage Support gem will improve the damage of the animated sword (but not of you when you're attacking with it). The upgraded Dancing Duo variant summons two copies of the sword, not just one.
As a build-maker, you can build around the idea that you'll usually be Unarmed, which allows you to use other special items like the Facebreaker gloves (see below). Alternately, you can use the Dancing Dervish as part of a generalized minion build, and just consider it an extra minion for your army.
The Dancing Dervish is a common drop, and is usually not too expensive. Dancing Duo is slightly pricier, but within what a new player could typically afford by the time they reach the level (65) required to use it.
Look the storm in the eye and you will have its respect.
Mjölner is a one-handed mace that, as is appropriate for its namesake, has massively higher Strength and Intelligence requirements than is normal for weapons of its type. It adds additional Chains to your skills (see Pierce, Fork, & Chain for more on this) and triggers any Lightning Spell socketed into it when you hit with it. You can, for example, socket an Arc spell and trigger a bouncing chain lightning with each attack.
As a build-maker, you'll have to decide whether you're scaling Mjölner's own damage, that of its triggered spells, or both (for example, by converting the Physical damage of your melee attacks into Lightning damage, then scaling that). You'll also need to decide which of the many Lightning spells to use.
Mjölner is a middling uncommon drop, but is usually within the range of what a new player could afford by the time they reach its level requirement (60).
Fly like a Storm Crow, crush like a Rhoa.
Facebreaker (often called Facebreakers but that's not the official name of the item) is a pair of gloves that add a gigantic boost to your Physical Attack damage, but only when you're hitting with your bare fists - it does nothing if you're hitting with a weapon. Most Facebreaker builds either leave their weapon slot empty and use a shield or quiver, or use a Dancing Dervish (see above) and melee on their own once the Dervish has animated itself.
As a build-maker, you have to compensate for the fact that your Unarmed attacks deal very little base damage and have 0% base Critical Strike Chance (meaning that, by default, Increased Critical Strike Chance will do nothing - see the page on Critical Strikes for more explanation). Added Physical Damage to Attacks becomes your most powerful stat.
Facebreaker is a common drop, and can usually be acquired very cheaply. It also has a very low level requirement and can be used by early Act 2.
Sire of Shards
That which was broken may yet break.
Sire of Shards is a Staff that adds many additional Projectiles to skills socketed in it, but makes those Projectiles fire in a nova in all directions instead of in a cone in a targeted direction. This can be bad (say, if you're at a distance and want to aim at a pack) or good (say, if you're throwing traps that explode in the middle of a pack). Other items often provide interesting numerical options, but Sire of Shards changes the behavior of socketed skills in a more fundamental way.
As a build-maker, you'll have to figure out how to take advantage of the extra projectiles and to get the most out of every direction of the resulting nova. Sire of Shards obviously makes no sense without a primary Projectile skill, but your choice of which one - usually a Spell, since Sire itself deals very little damage if you attack with it - is wide open.
Sire of Shards is a relatively common drop and is usually available at low price.
Tears of blood, aching heart, / My dear Isildria must depart.
Death's Oath is a unique chest armor that grants a special Death Aura skill. Death Aura is, as the name implies, an Aura, and is unique among Auras in that it is a damaging effect - it deals Chaos Damage over Time to nearby enemies. Like other item-granted skills, Death Aura benefits from any Support gem socketed in Death's Oath, regardless of links. This boost doesn't come free, however, and you take significant Chaos Damage over Time yourself when you kill an enemy.
As a build-maker, you'll want to maximize the damage of the Aura and its coverage by gaining bonuses to Chaos Damage, Damage over Time, and Area of Effect. Since Death Aura is an Aura, bonuses to Auras - like their area and effect strength - also affect Death Aura.
Death's Oath is an uncommon drop, but should be affordable to new players by the time they reach its level requirement (62).