As someone who has played Dota for several years on and off, played League of Legends for several months and has had access to the Dota 2 invite-only beta, playing the latter brought back a lot of nostalgia and a sense of respect for what both games (Dota & LoL) have to offer. Of course there are similarities between the two - since they are part of the same genre, but this isn't a thread about which is better. This is just a little list to show where the summoner spells came from in Dota (if they did have a similar effect). In most cases, the same effects came from active items in Dota. Enjoy! If I have made a mistake please correct me!

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This one actually did not have a corresponding active item ability. There are no abilities or items that directly reduce attack damage or ability/item damage instantly*, but the most similar is an ability called Static Link (his W) from an agility hero named Razor that drains your attack damage while also adding it onto his for a certain duration. As for the movement speed decrease component - this is quite a common effect in the game. There is an item called Diffusal Blade that slows enemies for 4 seconds on use. There's even a recently added item that slows the enemy (this was only 2 weeks back).

[CENTER]Diffusal Blade
+ 22/26 Agility
+ 6/10 Intelligence
Feedback (passive)
Purge (active)
Feedback
- Causes your attacks to burn 20 (36 when upgraded) mana and deal bonus physical damage equal to the amount of mana burned
- Orb effect and buff placer

Purge
- Purges a target unit, removing buffs, slowing, and dealing damage if it is a summoned unit
- Deals 99999 damage to summoned units
- Non-hero units will be paused for the first 3 seconds instead of slowed
- Slow lasts 4 seconds, Purge has a 8 second cooldown, and a 600 cast range

Rod of Atos
+ 25 Intelligence
+ 250 Health
Cripple (active, target unit)
- Slows the target's movement speed by 50% for 4 seconds.
Costs 50 mana, has a 20 second cooldown, and a 800 cast range[/CENTER]

* There is actually an ability called Whirling Death (his Q) from one of the newest heroes added a few weeks ago called Rizzrak, that reduces your primary attribute (that reduces your attack damage instantly for 7 seconds).

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The equivalent would be the phase boots, which is a much more spammable version of Ghost. Another item called Janggo of Endurance also gives a 10% AoE ghost on a 30 second cooldown.

[CENTER]Phase Boots
+ 60 movement speed
+ 24 damage
Phase (active)
- Gives 16% movement speed bonus and lets you move through units
- Using items or abilities cancels Phase
- Lasts 4 seconds, has a 8 second cooldown[/CENTER]

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The equivalent would be Mekansm.

[CENTER]Mekansm
+ 5 All Attributes
+ 5 armor
Mekansm Aura (passive)
Heal (active)

Mekansm Aura
+ 4 HP regeneration
500 AoE

Restore
- Heals 250 HP and gives +2 armor in 750 AoE
- Armor bonus lasts 25 seconds
- Heal does not affect units that have been healed by any Restore in the last 25 seconds
- Costs 150 mana, and has a 45 second cooldown[/CENTER]

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The Baron of Dota - namely, Roshan drops a one-use item called the Aegis of Immortality. There is also one hero named Skeleton King whose ultimate ability revives him.

[CENTER]Aegis of Immortality
Reincarnation (passive)

Reincarnation
- Brings you to life with full health and mana 5 seconds after you die, at the location where you died
- Aegis of the Immortal is removed from your inventory after reincarnating you once
- Aegis of the Immortal is also removed from your inventory when Roshan respawns (10 minutes after he was killed)[/CENTER]

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The equivalent is the Hand of Midas. Doombringer can also eat a minion as an ability gaining extra gold when fully consumed.

[CENTER]Hand of Midas
+30 attack speed
Transmute (active)

Transmute
- Kills a target non-hero non-ancient unit, giving bonus gold and experience
- Gives 1.5 times the unit's normal experience as additional bonus experience
- Gives 190 reliable gold (you do not get the normal creep bounty)
- Has a 100 second cooldown[/CENTER]

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While the concept of Ability Power as a core stat does not exist in Dota, the concept of amplifying your magic damage is done through more active means off of active abilities or items. There are a number of heroes and items that increase your magic damage towards one or multiple targets. (eg. Dragonus has a 36% magic amp ability, Veil of Discord actively amps all magic damage done towards targets affected by the debuff by 25% for a short period of time etc.) As for the the attack speed increase, there are also many passive abilities that buff that as well as a hero's ultimate (Troll Warlord's ultimate) that globally increases attack speed for all allies on the map for a short duration.

[CENTER]Veil of Discord
+ 5 armor
+ 5 HP/sec regeneration
+ 12 Intelligence
Discord (active)

Discord
- Applies a debuff on all enemy units in a 500 AoE, causing them to have reduced magic resistance for a duration.
- Amplifies magic damage by 25%
- Lasts 15 seconds, costs 75 mana, has a 30 second cooldown, and an 875 cast range[/CENTER]

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There are no items that can do this in Dota, but there is an ability (his W) from a new hero called Tresdin, that removes all debuffs and disables from a target ally (including himself) and on top of that, gives a heal-over-time and an increase to attack speed for a few seconds. There are no abilities or items that lower the duration of cc abilities.

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The equivalent is called Arcane Boots (formerly Arcane Ring).

[CENTER]Arcane Boots
+ 65 movement speed
+ 250 Mana
Replenish Mana
- Restores 135 Mana to allies in 600 AoE
- Costs 25 Mana
- Does not work on Meepo clones
- Has a 45 second cooldown[/CENTER]

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The only item that I can think of is the Urn of Shadows.

[CENTER]Urn of Shadows
+ 50% mana regeneration
+ 6 Strength
Soul Release (active)
- Whenever an enemy hero dies within 1400 AoE, gains 2 charges if it has 0 charges, else gains 1 charge (each death can only charge one of these items, if two or more heroes in the AoE have this item, only one will be charged)

Soul Release
- Can expend one charge to target an allied or enemy hero
- If an ally is targeted, it is healed for 400 HP over 8 seconds (this effect ends if the hero takes damage from a source other than Sentinel, Scourge or neutral creeps)
- If an enemy is targeted, it loses 150 HP over 8 seconds
- Has a 10 second cooldown, and 950 cast range[/CENTER]

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Non-existant in Dota.

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Although there aren't any direct items that temporarily reveal sight in an area - there are numerous global range abilities such as Clockwerk's Rocket Flare that does damage in an area and reveals that area for a short duration. There is also an item called the Bloodstone. If you die carrying this item, it will temporarily reveal that area until you respawn.

Bloodstone
+500 HP
+400 mana
+8 HP/sec regeneration
+200% mana regeneration
Starts with 6 charges.
Bloodpact (passive)

Bloodpact
- Bloodstone gains 1 charge each time an enemy hero dies in 1600 AoE
- Each charge gives 1 Mana regeneration per second
- When the bearer dies, Bloodpact restores 400 + 30 per charge HP to allied units in 1675 range, and Bloodstone loses a third (0.333) of its charges (rounded down)
- While dead, the bearer gains 1800/1800 AoE vision at the location of death, and gains experience in 1000 AoE at that location
- Gold lost on death is reduced by 25 per charge
- Respawn time is reduced by 4 seconds per charge
- Bloodpact only functions for the highest priority Bloodstone in the inventory

Everybody's favourite flash is arguably a less powerful version of the Blink Dagger! The difference, however, is that flash can work while attacked by enemy champs while the Blink Dagger can only be used if not attacked by enemies within 3 seconds, not to mention it takes up an entire item slot for just the flash effect!

[CENTER]Blink Dagger
Blink
- Teleports the caster to a nearby location instantly
- 1200 range
- Cannot be used if the carrier was damaged by an enemy player-controlled unit in the last 3 seconds
- Self damage does not disable Blink, but damage from Roshan does
- Costs 75 mana, has an 14 second cooldown
[/CENTER]

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Summoner's Insight - Reduces cast time by 0.5 seconds (for a 3.5 second cast time).[/QUOTE]
The equivalent is a Scroll of Town Portal. Scrolls of Town Portals function to go back to base or out to turrets. Boots of Travel permanently have an in-built effect that also has a 5 second reduction on its cooldown to 60 seconds, instead of 65*.

[CENTER]Scroll of Town Portal
Teleport
- Teleports you to an allied building
- Can be targeted at a point up to 525 range away from the building instead of directly on it, it will teleport you to that spot instead
- If the targeted point is closer than 50 range to the tower, 70 will be used as the distance from the tower instead
- When you use Teleport, the minimap is pinged for your allies at the target location of your teleport, and you are given 200 AoE vision at the target location for the duration of the teleport
- When the teleport finishes, trees are destroyed around the landing spot in a 480x480 square
- The casting time of the teleport is determined by how many allies have targeted a Scroll of Town Portal in a 1100 AoE around your target location in the last 25 seconds
- For each recent allied teleport in the area, time is added to your Teleport's casting time (2 seconds for the first recent allied teleport, 1 second for each additional one), the default casting time is 3 seconds
- Recent allied teleports have no effect if the target is in the fountain area
- Shares cooldown with Boots of Travel
- Costs 75 Mana, and has a 65 second cooldown[/CENTER]

*In addition, Boots of Travel allow you to teleport to both allied buildings and minions!

There are a few more, like Fortify that got removed. Fortify has a 5 minute cooldown in Dota and is called the Glyph of Fortification and makes your buildings invulnerable for 4 seconds. The entire team may access it at any time.

This is new.

Also.

http://leagueoflegends.wikia.com/wiki/Alpha_items

Riot had the right idea in the beginning.

I miss faceclam

Petition it to riot to have them unban him.

I'm having difficulty associating this name with the faceclam personality. You need to prostitute your body for $20 so you can change that account name to something else and this one to faceclam.