Counters can be removed.
However, I believe there is only one card that currently removes poison counters, and that is Leeches Target player loses all poison counters.
Leeches deals 1 damage to that player for each poison counter removed in this way.
Leeches was in the Homelands set.
boardgames.stackexchange.com/users/40/Pat Ludwig
Another way to reduce the number of poison counters that you have is through an effect that restarts the game, like Karn Liberated 's third ability.
Doing so resets your number of poison counters to zero, as per the New Phyrexia FAQ.
boardgames.stackexchange.com/users/25/Jadasc
Check out this column, by Magic head honcho Mark Rosewater: Something Wicked
This Way Comes .
It explains some of the thinking behind "modern" poison, most relevantly why you'll have trouble finding any other card that can reduce your poison total apart from Leeches.
Here's a taste:
My hatred of Leeches did one important thing.
It cemented in me the importance of poison not just being another life total.
(This theme will become very important in Scars of Mirrodin's design.)
As such, you will not see any card in the entire Scars of Mirrodin block that removes poison.
It cannot be done.
There are answers.
There are ways to deal with poison but healing yourself of it is not one of them.
If you want to remove poison counters you will only have one way—Leeches.
boardgames.stackexchange.com/users/436/thesunneversets
This answer is an attempt to create a canonical list: Leeches (Mark Rosewater intended this to be the only way to get rid of poison counters, but it no longer is) Karn Liberated (his -14 ability removes all poison counters, among other things) Suncleanser + a way to control their turn (such as Mindslaver )
+ a way for you to have your opponent control Suncleanser's ability (such as Bazaar Trader + Coffin Queen + Urborg, Tomb of Yawgmoth ).
An example of this combo is: put Suncleaner in your graveyard, take over their turn with Mindslaver, use Bazaar Trader to give them control of Coffin Queen, and then have them use Coffin Queen and mana from Urborg, Tomb of Yawgmoth to reanimate Suncleanser, chosing you to lose all your counters (which you can do because you control their turn).
Price of Betrayal + a way to control their turn (such as Mindslaver )
+ a way to get them to cast it (such as Hive Mind )
Honorable mention:
any of the cards that say "You can't lose" can allow to be alive (at least temporarily) with 10 or more poison counters.
boardgames.stackexchange.com/users/9999/Zags
And now, enter Suncleanser .
This will be released in M19.
It is a Cleric for 1W that will remove all counters from target opponent.
It can be found here, in the M19 gallery .
Now you can just get rid of all the poison counters.
Just like that.
For 1W.
On an opponent.
boardgames.stackexchange.com/users/23232/MarsJarsGuitars-n-Chars
A wild Price of Betrayal appears!
for B you can remove 5 counters from target artifact, creature, planeswalker or opponent
so maybe another one to add to the mindslave setup.
boardgames.stackexchange.com/users/29622/Bal The Barbarian
Is there some way to remove or counteract poison counters? Specifically, once you've already accumulated them, not when you are dealt them.  For example, say I already have 9 poison counters. Is there some way to reduce this number?
Can poison counters be removed?
boardgames.stackexchange.com
<magic-the-gathering>
boardgames.stackexchange.com/questions/4263
boardgames.stackexchange.com/users/1594/cha0sys
The Leeches card can remove poison counters. The only card that currently removes poison counters is  Leeches and the target player loses all poison counters.  Another way to reduce the number of poison counters that you have is via an effect that restarts the game, like  Karn Liberated 's third ability.
I believe there is only one card that currently removes poison counters, and that is  Leeches and the Target player loses all poison counters.   Another way to reduce the number of poison counters that you have is through an effect that restarts the game, like  Karn Liberated 's third ability.