While House of the Dead franchise is known for its Excuse Plot, it does actually have a storyline (a quite tangled one, too). Here you have it:
Sometime in 1991, a mad scientist known as Papa Caesar unleashed a plague somewhere in Louisiana that turns the resident into bloodthirsty mutants. Rookie AMS agent, G, is sent to deal with the problem, teaming with a local detective, Issac Washington, who has a vendetta against Caesar for killing his father. Their trail leads them to an abandoned house where Caesar is forcing a crippled genetic scientist, Jasper Guns, to make the plague. When Caesar makes a threat on Jasper's sister, Jasper mutates himself in hopes of stopping him. However, G and Issac bust in at the worst moment, turning Jasper's fury on them while Caesar escapes. They manage to stop and mercy kill Jasper not long after his sister, Varla, arrives, now gaining her own grudge against Caesar. G and Issac follow Caesar's trail of destruction with Varla not far behind (who has her own unrelated adventures battling the mutants with Jasper's girlfriend, Candi Stryper). However, she soon winds up captured by Caesar.
The trail leads the group to a prison, where it's revealed that Caesar was working for the warden, Clement. Clement kills Caesar, robbing Issac of his revenge, before explaining that the whole outbreak was a cause of trying to find a cure for his ailing mother. Clement discovered the plague underneath his prison in a secret bunker, an abandoned lab from the Cold War that was trying to create Super Soldiers, and gave the super soldier formula to Caesar. Clement takes Varla to be his guinea pig while G and Issac are forced to fight their way to his underground base. They arrive too late to stop Clement from transferring his mother's brain into Varla's body (Varla now nothing but a brain in a jar). However, the experiment goes wrong and Clement's mother mutates into a gigantic grotesque being. G and Issac manage to kill her, and the distraught Clement asks to atone for his actions by "going back into (his mother's) womb". G and Issac allow him to (mostly because he also had a bomb on him) while G takes Varla's brain and sets out with Issac. However, Caesar left a tape for Issac explaining that Clement had "powerful friends" backing him, so the whole ordeal was just the beginning. He also mentions that his father is still alive...
Seven years later, on December 18th, 1998. AMS agent Tom Rogan and his partner G are sent to deal with a disaster at the converted mansion laboratory of famed geneticist Dr. Roy Curien. Summoned by a distress call from Rogan's fiancee, Sophie, the pair discover the mansion is brimming with droves of undead (and other abominations) created by Curien's research into the unknown. Fighting through the mansion, the agents eventually confront Curien just as he's releasing his final masterpiece: The Magician. The creature promptly kills Curien, believing itself to be superior, and — after a lengthy battle — is destroyed by the agents. It's all over. The End... Or Is It??
On February 26th in the year 2000, the madness begins again. Agent G had tracked remnants of Curien's operation to Venice. When G goes missing, AMS rookies James Taylor and Gary Stewart are sent to investigate and discover that a much larger undead horde has descended upon all of Venice. The pair set off to stop whomever is behind the resurrection of Curien's work. Through G's notes and further investigation, it is discovered that Curien's work was funded by Caleb Goldman, the sinister CEO of the DBR Corp. However, Goldman is not interested in monetary gain - rather, he believes that mankind has inflicted too much damage to nature to be allowed to exist at its present capacity, and so he plans to kill off most of the global population.
Goldman saw great promise in Curien's work, and so he has fused Curien's experiments in genetic manipulation with his own work on the human genome. The resulting army of undead threatens not only Venice, but the entire globe. The AMS agents fight their way through the older sections of Venice - losing comrades along the way - before making it to Goldman's private skyscraper. James and Gary are then pitted against a resurrected Magician before confronting Goldman himself; Goldman unveils The Emperor, a supremely powerful creature designed to rule over nature and "destroy and hate mankind". Upon the demise of The Emperor, Goldman commits suicide... but not before pledging that a successor would come. Just the ravings of a madman, right...?
Three years later, James Taylor and AMS newcomer Kate Green are gathering information at the fifth basement of the AMS's European branch; James still has the events of the "Goldman Case" on his mind. Suddenly, the building is shattered by an earthquake and infiltrated by undead creatures that look an awful lot like the monsters Dr. Curien's work loosed on the world; they've already turned the surrounding area into a ruined wasteland. It gets worse when Taylor and Green discover that a nuclear launch is imminent; mutually-assured-destruction is about to glass the globe. Who is responsible for all this? It turns out that Goldman is responsible - from beyond the grave - for everything. James and Kate rush to Goldman's old headquarters to avert the nuclear launch, but Goldman has one last trick up his sleeve: a project codenamed Pandora's Box. The project is opened, revealing The World. Even though James and Kate square off against the monstrosity in an epic battle, weakening it greatly, The World refuses to die, forcing James to sacrifice his life to destroy The World in a massive explosion. The human race manages to survive yet again, but at the cost of one of its heroes.
As Kate is leaving the area, she runs into James' old partner G. Turns out Goldman had ANOTHER backup plan in case The World was destroyed. The two fight their way through the city, where they find another laboratory and face off against an old nemesis, The Magician, who plans on releasing clones of itself through the world upon their completion. G and Kate battle against him in a race against time to stop the clones. They succeed and set out to try and find survivors. Surely this was the end, right?
Fast-forward to 2019. Things have gotten much worse since the turn of the millennium; the massive zombie hordes that Goldman posthumously unleashed have brought about worldwide collapse. Tom Rogan managed to track down the source of the endless zombies to an abandoned, monolithic facility. He takes an experienced strike team with him... and doesn't return. Cue his daughter, Lisa, teaming up with Agent G to storm the place and bring her father home safely. Flashbacks reveal the original catalyst that drove Dr. Curien into his dark research: he sought to save the life of his terminally ill son, Daniel. Lisa and G reunite with Rogan and then team up with the now-adult Daniel to destroy Curien's final undead legacy: The Wheel of Fate.
The story is far from over, though; who knows what will happen next...