There were actually two known Muramasa Blades in existence. The first existed during one of Wolverine's adventures in Madripoor.
However, this blade was not the same blade presented to Wolverine by Muramasa himself. The first Muramasa Blade, often referred to as the Black Blade, was many centuries old. This original blade was forged by Muramasa using a piece of his own soul and granted a number of superhuman physical attributes to the one who wielded it. Muramasa, who has been stated as being quite mad, also poured his madness into the blade. After wielding the sword for a period of time, the wielder would slowly be overcome by the sword's influence. Wolverine wielded the sword briefly and quickly fell under its influence. Wolverine managed to reassert his will over the sword just as he was about to kill the Silver Samurai and Jessica Drew and threw the sword into a wall. The Silver Samurai pulled the sword from the wall and, apparently, was chosen as its fated master. The Samurai noted that the sword was controlled by a person as equally driven as the sword itself. The fate of the sword is unknown as the Samurai was the last one known to have it in his possession but he was not seen using it again.
The second Muramasa Blade's location was revealed to Wolverine by the Silver Samurai. This sword, currently wielded by Wolverine, was a sword forged specifically for him by Muramasa. On their first meeting in Japan, Wolverine came to Muramasa after his wife Itzu had been murdered, so he could help him to "kill 'em all". Muramasa accepted, and promised to forge him a "mighty blade -...- against which all... even one as great as you... will fall" using a piece of Wolverine's soul. When Logan came to claim the weapon, Muramasa gladly gave it to him, telling him to "wield it like an angry god".
Wolverine used it against a S.H.I.V.A. robot, cutting it in half with a single blow. Later research of the remains of the robot showed that it was not cut, but rather "sliced, on the molecular level". The scientist who was doing the research theorized, that the instrument could have been some sort of plasmic form. In a subsequent fight with Captain America, the sword was used against Wolverine, leaving a scar on his chest, which oddly didn't heal as usual. After the fight was over, Wolverine gave the sword to Cyclops, explaining it by saying: "This is the only thing in the world that can put me down for good."
When Sabretooth was literally insane, Wolverine took the sword from Cyclops and used it against Creed. After a short fight, and after Creed had killed Feral, Logan decapitated his foe, killing him. 
Cyclops and the X-men attempted to stop Wolverine's son, Daken, who was impersonating Wolverine in Norman Osborn's Avengers. Cyclops brought the sword with him, but this was secretly what Daken wanted. Daken obtained the sword for a short time, but Wolverine then retrieved it. Daken, however, was able to make off with a small piece of the broken blade. He sought out the Tinkerer to obtain his help in making use of that piece as a weapon.
Wolverine later took the blade again when Omega Red was hunting him. It came down to a final showdown and Logan stabbed Omega through the heart with the blade. Romulus then appeared and fought Logan. When Romulus was victorious, he threw the Muramasa Blade on the ground, stating he thought Wolverine would need it. After defeating Romulus, Wolverine cut the pieces of the Muramasa Blade out of Daken's arms and buried them and the rest of the sword in a secret location.
Properties of the Muramasa Blades
The Black Blade is many centuries old and possesses a variety of mystical properties that it possesses in and of itself and properties that it grants to those who wield it. Muramasa took a portion of his soul and used it in forging the sword. As a result, the blade also contains a portion of Muramasa's evil and madness. The alloy that the sword is made of is unknown and is black in color, but has shown to be virtually indestructible. The sword has withstood multiple blows from Wolverine's Adamantium claws and has struck his Adamantium-laced bones without sustaining any damage. The blade also grants superhuman physical strength and resistance to injury to whoever wields the sword. However, eventually, the madness and evil that Muramasa poured into the blade will eventually overcome the will and original personality of an individual if he or she has it for too long.
The second Muramasa Blade, the one currently in Wolverine's possession, was forged specially for him. Muramasa used a piece of Wolverine's soul in forging this blade, just as he used a piece of his own in forging the Black Blade. This sword is also made of an unknown alloy that was originally bright red in color, but now has the color of a conventional blade. However, much like the Black Blade, this sword is also extremely durable and is capable of cutting almost any substance. The blade has easily cut through the armor of a S.H.I.V.A. (Earth-616). robot on a molecular level and has also "sliced" one of Cyclops' optic beams into several different beams and reflected them in different directions. The sword is also capable of greatly reducing the efficiency of a superhumanly fast healing rate. Wolverine himself has stated that the sword is the only thing on Earth that can truly kill him. For example, during a battle with Captain America, Wolverine was injured with the sword. Though the wound was minor, it remained inflamed and didn't fully heal for a period of several days. Another, more recent example, involves Wolverine using the sword to slice off Sabretooth's right arm and to decapitate him moments later. Sabretooth attempts to hold his severed arm in place so that the tissues will reconnect, as he did after having his right hand sliced off by Wolverine's Adamantium claws in an earlier confrontation. The arm merely falls back to the ground. It is possible that, if given enough time, Sabretooth could have either reattached his arm or grown another one.
During the fight between Daken and the X-Men, it was discovered that the blade could not cut through Armor's psychic shield, which was powered by her ancestors' memories.