This page lists a number of example Skills 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.
In addition to the skills themselves, how you choose to deliver a skill's damage to your target is a major build option. Most Projectile Attacks and Spells, for example, can be loaded onto Totems, Traps or Mines that will use the appropriate skill for you, and these builds differ substantially from so-called "self-cast" builds.
You can read about the mechanics of these effects in the Mechanics Reference page on Totems, Traps, & Mines. Totem bonuses are found mostly in the upper-left portion of the tree, and Trap and Mine bonuses are mostly found in the upper-right. The Hierophant Ascendancy for Templars focuses on Totems, and the Saboteur Ascendancy for Shadows focuses on Traps and Mines.
Sometimes, you just need a little help from your friends! These skills summon Minions to fight for you. Minion passives can be found near the top of the passive tree, and the Necromancer Ascendancy for the Witch gives lots of Minion-specific bonuses. You can read about Minion mechanics here.
Raise Spectre: Allows you to resurrect a copy of an enemy monster to follow you permanently unless killed. You're limited to one Spectre by default, but various effects can add a few more. The monster retains all of the skills it had in life, and can use all of them at full power for you.
As a build-maker, you'll want to research which monsters make strong Spectres and synergize accordingly. For example, Spectres with lots of Area attacks could be paired with strong single-target minions (like Skeletons) to help against bosses.
Available in late Act 3 to all classes.
Mirror Arrow: Shoots an arrow that, on landing, summons a clone of you for a brief period. The clone uses a copy of your current bow and is considered a Minion for game-mechanics purposes (I note this here because not all clone effects work this way). There's no hard limit to the number of clones you can have summoned, but the skill has a cooldown and the clones have a limited duration, both of which effectively limit you to a handful at a time.
As a build maker, you should think about which Bow to use and try to stack the Increased Skill Effect Duration necessary to keep your clones around longer to hammer away at bosses and the Increased Cooldown Recovery to spam out more clones.
Available in late Act 3 to all classes.
Sometimes you just want to blow your enemies up with big elemental nukes. That's what these are for. Spell bonuses can be found mostly near the top of the passive tree (as can Elemental bonuses; most Spells deal Elemental damage). Many Ascendancies, like the Elementalist (Witch), Hierophant (Templar), and Inquisitor (Templar) offer Spell or Elemental bonuses. Most spells can be loaded onto Totems, Traps, and Mines to change the way you use them.
Winter Orb: Winter Orb is a Channeled skill that places an orb over your head. The orb will periodically shoot ice at nearby targets. Channeling for longer will make the orb more powerful; the orb slowly decays when you're not Channeling. You can use the Cast While Channeling Support gem to trigger other skills while you empower your orb.
As a build-maker, you'll want to look for things like extra Projectiles (since unlike most Projectile skills, multiple Winter Orb shots can hit the same target) or modifiers to Channeled skills (especially if you're not using it to trigger some secondary skill).
Available in late Act 3 to all classes.
Purifying Flame: Purifying Flame fires a wave of flame to a targeted location, then explodes on arrival in a much larger blast that leaves behind Consecrated Ground. By default, Consecrated Ground heals you and increases your Critical Strike Chance against enemies in it, but it also interacts with numerous other effects. Divine Ire deals Physical damage, then converts some of it into Fire damage. This means that it benefits from effects based on Physical damage, and in particular from effects that "Add X% of Physical Damage as Extra <Type> Damage".
As a build-maker, you'll want to focus on taking advantage of these unique attributes. Can you find items with bonuses while you're on Consecrated Ground? Can you abuse extra Life Regeneration? Can you stack lots of conversion and added-as damage effects to use the fact that it deals base Physical damage?
Available at the start of the game for the Templar, and in late Act 3 for other classes.
"Hah!" thought Thog. "Wizards dumb. Playing with silly magic. Put so much effort into head, they forget that club beats head!" He paused for a moment. Maybe, he thought, he might be wrong. Maybe there was some benefit to learning some of those 'letters' he'd heard the village elder going on about. He pulled his club out of the bloody stump left atop the wizard's shoulders. He'd think about it later.
Get up close and dirty with an axe, a sword, or a hammer. The legions of evil have squishy bits, and you have a thing that is less squishy than their bits. Melee bonuses can be found mostly in the bottom half of the tree, and most of the Ascendancies for the Marauder and Duelist benefit Melee skills.
Molten Strike: Molten Strike hits an enemy, then causes four small balls to fire from that enemy. They impact the ground nearby, dealing damage to nearby enemies (potentially including the original target). As the name suggests, it also converts much of your Physical damage into Fire damage. The initial hit deals Melee Attack damage, and the balls deal Projectile Attack damage; both deal damage with your weapon and thus both benefit from damage with melee weapons (as opposed to melee damage).
As a build-maker, you'll want to consider how you want to scale the skill. Do you want to focus only on scaling the Projectiles, as most Molten Strike builds do, or do you want to stick to effects that benefit both? You can abuse the large number of possible hits from the skill to gain lots of Life through Life Gain On Hit or to apply numerous other on-hit effects. You can also use effects like Ancestral Call Support to hit multiple enemies and thus add more balls per attack.
Available almost immediately for the Duelist, Marauder, Templar, and Scion. Available in late Act 3 to other classes.
Earthquake: Earthquake strikes an enemy and leaves an "aftershock" below their location. The aftershock detonates after a brief period, dealing heavy damage. Attacking again before the aftershock triggers won't create another aftershock - you can only have one at a time - so Earthquake benefits from very slow attack speed.
As a build-maker, you'll want to find effects that reduce Skill Effect Duration to cause your aftershocks to trigger more quickly, and to use the skill with a very slow weapon to ensure your attack speed stays slower than your aftershock trigger time.
Available in late Act 3 for all classes.
The shield crab does not leave his shell unless it is forced to, and even then, it knows to keep its distance.
What kind of idiot wants to get close to their target? No, siree, you're a smart one. You'll pass on being hit by cosmic monstrosities and living piles of desecrated blood. Most Projectile Attacks use a Bow, but a Bow isn't the only option. There are also a few Attacks based around Wand projectiles and even a couple that use melee weapons to deal damage at range. Projectiles can be modified in a number of ways, most notably through adding Additional Projectiles and through the Pierce, Fork, & Chain effects.
Projectile bonuses can be found mostly on the right-hand side of the tree. The Deadeye Ascendancy for Rangers focuses heavily on Projectile Attack bonuses.
Spectral Throw: Spectral Throw throws a copy of your melee weapon in a targeted direction. The weapon flies a set distance, then turns around and boomerangs back to you. Unlike most Projectiles, a single Spectral Throw Projectile can hit an enemy more than once (though there's a delay before an enemy can be hit again), allowing one of your Projectiles to hit once on the way out and once on the way back. Spectral Throw always Pierces, and therefore can't Fork or Chain. It can, however, have additional Projectiles added to it, causing you to throw a wave of weapon copies in a clone.
As a build-maker, you'll want to seek out bonuses to Melee Weapon Damage (but not Melee Damage - Spectral Throw deals Projectile damage despite using a Melee Weapon). You can dramatically increase the range of your Spectral Throws with increases to Projectile Speed, or somehow take advantage of the skill's large number of Hits.
Available to all classes except the Witch immediately. The Witch can acquire it in late Act 3.
Lightning Arrow: Lightning Arrow fires an arrow that, on impact with an enemy, zaps three nearby enemies with a jolt of lightning that deals the same amount of damage as the initial shot. This zap triggers on every hit of the initial arrow, meaning that if the initial arrow Pierces and hits more than one target or Chains to a secondary target, it zaps nearby enemies again. Both the initial shot and the zaps deal your weapon damage and convert a portion of your Physical damage into Lightning.
As a build-maker, you could focus on adding extra Projectiles, or causing them to Pierce, Chain or Fork, to maximize the number of zaps triggered against a large pack. Larger Area of Effect makes the zaps reach further. You can also take advantage of the conversion of your Physical damage into Lightning to build a Lightning-centric attack build.
Available to the Shadow, Ranger, and Duelist near the end of Act 1, and to other classes in late Act 3.
Tornado Shot: Tornado Shot fires a Piercing arrow that, upon reaching the target location, explodes into a nova of additional arrows. Adding more Projectiles adds more of the initial arrows, resulting in more novas. Enemies can be hit by at most one arrow from each nova, but can be hit multiple times by arrows from different novas, making Tornado Shot particularly effective against single targets relative to other Bow skills.
As a build-maker, you'll want to maximize the number of Projectiles you fire without sacrificing too much damage. The large number of hits from Tornado Shot makes effects like Life-on-Hit particularly strong.
Available to all classes near the end of Act 3.