How can I avoid damage from Sniper's Ultimate?

What are the ways we can avoid getting hit by Sniper's Ultimate ability, Assassinate? Which items and/or hero abilities can be used to escape it once it has locked on to a hero?

There're several ways to do this, most require low ping & fast reflexes:

By Disjointing

In DotA, disjointing consist in removing oneself from being the target of a projectile. This can be achieved in several ways :

• By blink dodging if you blink as soon as it hits / split second before. This works with Queen of Pain, Anti Mage, Blink Dagger, Slark's Pounce, Mirana's Leap, Puck's Etheral Jaunt, Storm's Ball Lightning or Morphling's waveform, Nature's Prophet Teleportation.
• By creating illusions : With Manta Style you get a brief period of invulnerability when you use it, CK's Phantasm will give you 0.5s, Naga Siren's Mirror Image will give you 0.3s.
• By Banishing yourself : Lifestealer's infest or Puck's Phase Shift
• By Transforming yourself : Abilities that morph your hero grant some tiny frames of invulnerability so if timed well you can transform disjoint with : Chemical Rage (Alchemist), True Form (Lone Druid) and Metamorphosis (Terrorblade)
• Becoming invisible will disjoint projectiles but not Assassinate (since Assassinate gives true sight of the target)

Blocking the damage

• With a skill like : Ember Spirit's Flame Guard (up to 500), Abaddon's Ultimate (Borrowed Time), Abaddon's Apotic Shield or Templar Assassin's Refraction.
• With an item : Like Pipe of Insight.
• By becoming magic imune : Black King Bar, OmniKnight's Repel, LifeStealer's Rage.

By Becoming invulnerable :

Invulnerability is granted by several skills (and Eul's Scepter) in the game. You can become invulnerable by

• Being disabled : Using Eul's Scepter on yourself, same goes if you get Nightmared by Bane, Slept by Song onf the Siren, Disrupted (Shadow demon) or Astrast Emprisonned by Outworld Devourer etc (full list on the link).
• Being hidden : During Juggernaught Ultimate, or Ember's Sleight of Fist, Lifestealer's infest or Phoenix's Supernova(full list on the link).
• Some blink grant invulnerability : Void's Timewalk or Tuskar's Snowball (for example).

By Blocking the Spell completely

If you have a Linken's Sphere or an ally uses his to buff you, the spell will completely be cancelled.

Note that all these also apply to most single-target spells

Sniper's ultimate Assassinate is single target magic damage. Anything that blocks single target spells or makes you immune to magic damage will prevent it and it's damage can be reduced through magic resist such as cloak, hood, or pipe. The projectile, while fast, can be disjointed. Sniper can also be interrupted as it's a channeling ability prior to firing.

The request for specific hero abilities who can avoid it is somewhat unreasonable because there are so many. Look at the heroes you like to play and dig into their abilities. Anything that allows for disjoints (blinks, tornadoes, removals, invulnerabilities, slark's ult) can dodge the in air bullet with timing.

The quick list of items that can help you with the damage is: Hood, Pipe, Linkens, Euls, BKB, TP, Manta, Blink, Bloodstone, and finally if you're losing stack bracers.

You can :

• Disjoint the projectile (Except by becoming ivisible since Assassinate gives true sight of the target)
• Become Invulnerable
• Become Magic Immune
• Block damage with spells such as : Apotic shield (Abaddon), Ember Spirit's FlameGuard, or Templar Assassin's Reflection or an item like Pipe
• Block the spell with Linken's Sphere