Proliferate is a keyword action introduced in Scars of Mirrodin. When a player proliferates, he or she chooses any number of players and/or permanents with a counter on them, then puts another of those counters on these players or permanents.  In Scars, proliferate only appeared on blue and artifact cards. In Mirrodin Besieged, it shows up in black and green (one card each). 
For example, a player proliferates and chooses an opponent with a Poison counter, a Planeswalker card with a loyalty counter, a creature with a -1/-1 counter and an artifact with a charge counter on it. Then that opponent gets another poison counter, the planeswalker gets another loyalty counter, the creature now has two -1/-1 counters and the artifact two charge counters on it. Note that proliferate does not target, so permanents with shroud or hexproof can be chosen.
Thematically, the Proliferate mechanic is tied in with the Phyrexia faction in Scars of Mirrodin and its related Infect mechanic. As such, each of the cards that have been printed with proliferate are marked with the symbol of the Phyrexia faction. Only featured on blue and artifact cards in Scars of Mirrodin, it has spread to black and green in Mirrodin Besieged, illustrating the block theme/storyline of the Phyrexian infestation taking over Mirrodin.
- You can choose any player that has a counter, including yourself.
- You can choose any permanent that has a counter, including ones controlled by opponents. You can't choose cards in any zone other than the battlefield, even if they have counters on them, such as suspended cards or a Lightning Storm on the stack.
- You don't have to choose every permanent or player that has a counter, only the ones you want to add another counter to. Since "any number" includes zero, you don't have to choose any permanents at all, and you don't have to choose any players at all.
- If a permanent chosen this way has multiple kinds of counters on it, only a single new counter is put on that permanent.
- Players can respond to the spell or ability whose effect includes proliferating. Once that spell or ability starts to resolve, however, and its controller chooses which permanents and players will get new counters, it's too late for anyone to respond.
- When you proliferate in a Two-Headed Giant game, you may give one poison counter to a team that already has one.
The latest reminder text for proliferate reads "You choose any number of permanents and/or players with counters on them, then give each another counter of a kind already there."
Mark Rosewater originally developed a mechanism for creatures to amplify infect by adding -1/-1 counters to those already on other creatures. This mechanism futhered the metaphor of a Phyrexian disease spreading. Eventually, it grew to affect all counters.  
Cards with Proliferate
|Contagion Clasp||Scars of Mirrodin|
|Contagion Engine||Scars of Mirrodin||The only card with an ability to proliferate more than once per activation|
|Inexorable Tide||Scars of Mirrodin||The first enchantment with proliferate|
|Steady Progress||Scars of Mirrodin||The first instant with proliferate|
|Thrummingbird||Scars of Mirrodin||The first creature with proliferate|
|Throne of Geth||Scars of Mirrodin|
|Core Prowler||Mirrodin Besieged|
|Fuel for the Cause||Mirrodin Besieged|
|Plaguemaw Beast||Mirrodin Besieged||The only green card with proliferate|
|Spread the Sickness||Mirrodin Besieged||The first sorcery and first black card with proliferate|
|Grim Affliction||New Phyrexia|
|Tezzeret's Gambit||New Phyrexia|
|Viral Drake||New Phyrexia|
|Volt Charge||New Phyrexia||The only red card with proliferate|
- Proliferate was featured as rules card 3 of 5 in the Scars of Mirrodin set, 5 of 5 in the Mirrodin Besieged set, and 4 of 4 in the New Phyrexia set.
- Mark Rosewater. (September 20, 2010.) "Something Wicked This Way Comes, Part 3", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Mark Rosewater. (January 24, 2011.) "Under Besiege, Part 2", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Mark Rosewater. (October 04, 2010.) "Proliferate Crazy Nights", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Tom LaPille. (October 08, 2010.) "Proliferate Expectations", Daily MTG, magicthegathering.com, Wizards of the Coast.