As of September 2014, the fusion monster "Armityle the Chaos Phantom" is the strongest Yu-Gi-Oh card, with 10,000 attack points during the controlling player's turn. This card has the highest original attack points, can't be destroyed by battle and takes three other high-value monster cards to summon.
Five "Yu-Gi-Oh!" cards have 5,000 original attack points printed on the cards, as of September 2014. "Five-Headed Dragon" requires five dragon-type monsters and "Polymerization" to be specially summoned. "Superdimensional Robot Galaxy Destroyer" has 5,000 original attack points after three level 10 monsters "xyz summon" the card, and this monster destroys all of the opponent's spell and trap cards.
Attack points of "Yu-Gi-Oh!" monster cards can be increased by card effects, spell cards and trap cards. "Strongest" does not mean "invincible," because every "Yu-Gi-Oh!" card has some type of vulnerability in advanced play, even with huge amounts of attack points.