Seto Kaiba is typically seen as a arch-villain of Yugi in the original Yugioh series. But as the story progresses he becomes a little more of an ally than an enemy.
Kaiba is the owner of his own company, called Kaiba Corp. Throughout the series Kaiba is in a constant struggle to maintain ownership of the company while dueling and creating enemies out of defeated duel opponents. Because of his constantly changing focus of attention, Seto Kaiba develops into a very complicated character.
Seto and his younger brother, Mokuba, were orphaned at a very young age and this leaves Seto to be fairly co-dependent on Mokuba. It is through Mokuba that we are introduced to a more human and sympathetic version of the character.
At one point, Seto is defeated in a duel by Yugi who uses a Exodia to defeat the Blue Eyes White Dragon, and subsequently retires from playing Duel Monsters. However, when Pegasus kidnaps Mokuba in an attempt to take over Kaiba Corp., Seto is forced to once again pick up his dueling deck and fight to free his younger brother.
Later, Seto Kaiba comes into ownership of Obelisk the Tormentor during the Battle City tournament and then plays further into the plot of the stone tablet and it's depiction of Yugi and the Egyptian God Cards. Ultimately Kaiba loses Obelisk the Tormentor to Yugi during the semi finals.
Though he does not appear in the series, Seto Kaiba is referenced in the GX series as the one who started the Duel Academy. Thus tying the two series together.