Many -- if not all -- of the issues presented in Final Fantasy VII can be linked back to the Jenova Project: a study of a supposed Ancient that went horribly wrong, to say the least. Pre-natal injections of alien Jenova cells were what made Sephiroth and the buster sword's original owner Angeal into monsters, and a similar technique was used to enhance later experiments known as the Sephiroth Clones. Cloud is one of these clones, and it was during this process that he attempted to escape with Zack.
It should be noted that the cells injected into Cloud and Zack during Hojo's experiments give them abilities and stamina similar to Sephiroth, and these enhancements are what classify them as clones. Unlike Sephiroth and Angeal, they were not actually conceived in as a result of the experiments. In fact, the lack of pre-exposure to mako and the Jenova cells proves to be near-fatal for Cloud.
Failed Case #2: Shinra Infantryman
Summary: Weak tolerance to Jenova cells led to toxicosis. Lack of response to outside stimuli suggests severe system damage. Recovery highly unlikely.
Even with that weak tolerance -- or perhaps because of it -- Cloud has a strong connection to Jenova. The presence of her cells weaken his already flailing psyche, using their mimic ability to help project the war hero persona (side note); they even enable Sephiroth to control Cloud's movements by manipulating the cells themselves. After involuntarily handing over the Black Materia and even raising his sword against Aeris, poor Cloud is haunted by the constant fear of an attack on AVALANCHE from the inside. He loves his friends and would never hurt them, but Jenova gives Sephiroth the ability to completely override such emotions. She is a powerful enemy that cannot be easily seen nor confronted.
In addition, all Sephiroth Clones have developed a biological timer set for the Reunion, a precursory event to Jenova's restoration to power. After learning of this and briefly falling in and out of sanity, Cloud begins to question his motives for tracking Sephiroth. Is he really striving to save humanity or simply giving in to his instincts to join the Reunion? Although a literal walk through his psych helps him evaluate his priorities to defeat of Sephiroth, it soon becomes clear that it takes more than sheer determination to overcome the threat of Jenova.
Geostigma
We learn in Advent Children that Jenova's descent into the Lifestream all those years ago caused her cells to disperse, contaminating the very essence of the Planet. When the Lifestream surged to the surface to confront Meteor during Final Fantasy VII's finale, hundreds, perhaps even thousands of people across the Planet were exposed to high quantities of the contaminated substance. When Sephiroth's strong spirit -- felled by Cloud -- is also returned to the Lifestream, the combination proves fatal, ultimately resulting in an epidemic known as Geostigma.
Cloud learns he has contracted Geostigma almost two years after the initial battle, no doubt the already high quantities of Mako and Jenova cells injected into him during the Jenova Project heightened his vulnerability to the disease. The illness inflicts tremendous physical pain, sometimes even causing him to black out completely. However, the emotional toll the Geostigma has over Cloud is what's ultimately devastating: he loses all hope in ever having a life. No matter how strongly he feels for it, because of Geostigma he abandons his life and family to die alone.
This is the power of Jenova. Even at the cellular level, her influence over the Planet will never totally die away so long as there is a strong will -- Sephiroth -- to wield it. Even if the cells can no longer dictate his physical actions as they did in FFVII, the spasms of pain and terrible visions are enough to completely halt Cloud's way of life, making him believe that he has no choice in the matter.
Dirge of Cerberus confirms that people across the Planet are still infected with traces of Geostigma, and the twisted experiments Jenova inspired still roam the underground. So long as even the smallest sample of her cells exists -- long after her physical form has been destroyed and scattered -- she will continue to poison the Planet and its people. However, with Sephiroth banished to memories, they are useless.
By the end of Advent Children, Cloud is comfortable with his life, realizing that everything is important to him -- his friends, his family -- and that he really does have a home. In Dirge of Cerberus, he has stepped down as leader of their rag-tag team, seen only in battle alongside his friends and heard over the phone as he tries to help Vincent coordinate their next plan of action. Despite the fact that Hojo's other experiments -- a painful reminder of his past terrors -- have declared war on everything and everyone, he appears surprisingly grounded throughout the latest fight for humanity. Although there is certainly still a part of him haunted by the Jenova cells and their omnipresent evil, his previous revelation of self has instituted new confidence.
For the longest time Cloud saw himself as a victim. He believed he could not fight Jenova's control; he could resist all he wanted to, but she would always be there in the end. However, during his final fight with Sephiroth, he realizes that he is above all that. He has people to love and a place to call home; he has a heart of his own, and with it he can leave Jenova and the horrible experiments he was subjected to behind. Sure, they will always be a painful part of his life, but now he is confident enough to face them and move on.
A side note: Jenova's Mimic Ability
Jenova's "Mimic" in relation to Cloud is never stated outright in the game but is explained with surprising detail in the Ultimania. I've been struggling to find a way to articulate this on Strife, because... honestly, I think the game progressed just fine without this explicit knowledge (I kind of liked the idea of Cloud being Just Plain Crazy instead of Crazy With 10% More Alien). However, the more I thought about, the more I think it's inclusion is to break the forth wall and include the player in Cloud's state of Batshit Crazy. More on this can be read in the Avatar section.
