The Millennium Falcon went through many different owners and pilots before it found its way to the smugglers turned war heroes who made it famous. The first owners of the ship were the Corell Industries Shipping Firm, who possessed the ship for about 12 years. While Corell Industries was using the ship, it gained a reputation among its different pilots as being both remarkably fast and incredibly unreliable. The ship went through a list of temporary names signifying these facts (Corell's Pride, Fickle Flyer, Meetyl's Misery, etc.). Eventually, however, Corell went out of business, and the ship was sold to Kal and Dova Bringer, a pair of smugglers. The Bringers made the first major modification to the ship, a bigger hyperdirve. The ship, now called the Hardwired was easily one of the fastest in the smuggling business, which brought it to the attention of Cularin's Smugglers Confederacy. After a failed deal with the Confederacy, Dova Bringer was killed in an attempt to take the ship. Kal, renaming the ship Wayward Son would later be killed during another run while working for Iaco Stark's Commercial Combine.
The next known owners of the ship were a group of Republic senators and Jedi during the Clone Wars called the Republic Group. The Republic Group employed two men, Jadak and Reese, as pilots of the ship. Both Jadak and Reese were believed killed when the ship (then called the Stellar Envoy collided with a large bulk freighter above the smuggler's moon of Nar Shaddaa (though Jadak did survive the wreck and would later go on to try to track the Envoy down). The ship sat destroyed in orbit o above Nar Shaddaa for about a year before it was salvaged by technician Bammy Decree. Decree completely rebuilt the ship, using parts from a YT-1300p frieghter and sold it the crime boss Rej Taunt who renamed the ship Second Chance.
The Chance was only in service to Taunt for one single smuggling run that ended in the ship being impounded by the Imperial Navy. It was stolen by ship thief Zenn Bein. During the next couple of years, the ship passed hands several times fairly quickly, belonging to several individuals including the Rebel Quip Fargil who gave the ship the name the Millennium Falcon before coming into the ownership of Doctor Parlay Thorp, who used the ship as a medical relief vessel to several planets that were oppressed by the new Imperial regime. Thorp would go on to sell the ship to Molpol's Traveling Circus before it found its way into the hands of Lando Calrissian.
Lando aquired the Falcon in a card game (which would ironically be how he loses the ship as well) from professional gambler Cix Trouvee, who ran out of money to cover his debt. Lando worked for several years as a small time smuggler, using the Falcon as his primary ship and base of operations. He later came into ownership of a ship lot selling luxury ships, were he left the Falcon as he went to the annual Cloud City Sabaac Tournament. During the tournament, Lando found himself in the same place as the man he won the Falcon from, and he placed a marker in on the table for "any ship on his lot". His friend Han Solo ended up winning the hand, and taking the Falcon as his prize.
Han and his co-pilot Chewbacca ended up making most of the major modifications to the Falcon. They replaced the hyperdrive with a millitary grade one, upgraded the basic laser cannons to two quad turbolasers mounted on the top and bottom of the ship, a pair of concussion missle launchers housed in the forward mandibled of the ship, and various sensor array and minor mechanical upgrades. They effectively turned the ship into the ultimate smuggling vessel, if an incrdibly finicky one. Han and Chewie would go on to make the ship famous in the smuggling world by making the Kessel Run in less the 12 parsecs, and being the best and fastest at their profession, if not the luckiest. The ship would later become famous across the galaxy when it was used in the destruction of both Death Stars and many other battles fought by Han and Chewie as they aided the Rebel Alliance and the New Republic after it.