The Demon Castle War (also known as the Battle of 1999) is first mentioned in Castlevania: Aria of Sorrow, and occurred in 1999. In the game, you can acquire and equip an actual uniform from the battle. Also, some enemies Soma Cruz encounters in Dracula's Castle - the Zombie Soldier and Zombie Officer - are the reanimated corpses of soldiers who died some 36 years before (indicating the date of the War, as the game is set in 2035). It remains unknown who these soldiers fought for during the War, although it is possible they opposed Dracula's forces.
The specifics of the war are never directly explained in the game, but it is likely that it involves the events that led Julius Belmont to defeat Dracula once and for all. Whether or not the exact details will ever be known remains a mystery, though it is known that Alucard (also known as Adrian F. Tepes) was also directly involved.
Furthermore, as an explanation for the Vampire Killer being entrusted to the Morris clan, Wind mentions, due to the predicted War in 1999, the Belmonts themselves were inexplicably forbidden to use their family whip for an indeterminate amount of time before (possibly starting from Castlevania: Bloodlines), with the Morrises and others forced to "fill-in" for eventual, premature, resurrections of Dracula.
There is no game in the Castlevania series which depicts or explains the events of the Demon Castle War at this time.
Besides Alucard and Julius Belmont, characters who would possibly have been involved in the war include Jonathan Morris, Charlotte Aulin, Stella Lecarde and Loretta Lecarde, though they would all be in their 70s. Saint Germain also hinted at being a visitor to the events leading to Dracula's destruction, and could therefore have been involved in the War or been a witness to it.