The following is my analysis of the similarities between Final Fantasy VII and the recent Square Pictures production Final Fantasy: The Spirits Within. THIS ANALYSIS CONTAINS MAJOR SPOILERS TO THE PLOT OF THE MOVIE. Here are my observations, in no particular order:

(and yes, this IS at least vaguely relevant to Jenova. :P)

1. Although I can't remember the exact details (I need to watch the movie again), Aki has something inside of her that came from the Phantoms. This is what causes her to dream of them so often, and start to lose her mind a little towards the end of the movie. This makes her very similar to the Jenova Project subjects in FF7 - they have a part of Jenova inside them, which causes them to be drawn towards the Reunion. They also start to turn a little insane shortly before the Reunion takes place - Cloud is the obvious example of this, when Sephiroth and Jenova start messing with his mind.
   
   
2. The Phantoms' nest on Earth is a huge crater, which was formed when the Phantoms crashed to Earth from their planet. The idea of a crater formed by something crashing down from another planet is exactly the same as the theroy of Jenova falling from the skies and creating the Northern Crater when she landed. Also, a connection can be drawn with the meteor the phantoms were on before they crashed: some people say that Jenova summoned Meteor before landing on the FF7 planet, and that was what created the Northern Crater. Also, the Phantoms living in the Crater is very similar to Jenova and Sephiroth - although physically dead - being very much alive in the Northern Crater.
   
   
3. Aki Ross has several similarities to Aeris (Aerith) Gaisborough. She understands the nature of how the Planet works and the theory of Gaia, just like Aeris could hear the Planet and understood the Lifestream. The main difference is, obviously, that Aki is still alive by the end of the story.
   
   
4. The Zeus Cannon used by General Hein to destroy the Phantoms can be compared to FF7's Siter Ray (Mako Cannon). In FF7, President Shinra (Rufus) used the Mako Cannon to destroy WEAPON, before Hojo tried to use it to give Sephiroth Mako energy. In the film, the Cannon explodes when Hein tries to fire it too many times and it becomes overloaded with Energy: just like the Sister Ray does in FF7 when Hojo tries to fire it for the second time. The actual characters of Hein and Hojo are also very similar at this point - both become so drunk with power that they become more than a little insane and stop caring about what happens as a result of their actions since they are so intent on achieving their goal. Not to mention, their names both start with H and have the same number of letters. =D
   
   
5. The whole Gaia theory, i.e. that the Planet is alive and can feel pain, very closely mirrors the Lifestream theory of FF7. The idea that all Souls return to the Lifestream is the same as the idea of all Souls returning to Gaia in the movie. When Gaia is actually seen, towards the end of the movie, it has a similar appearance to the Lifestream in FF7 (which you see after Mideel is destroyed) - the only difference being is that Gaia has a bluish colour, while the FF7 Planet's Lifestream is green.
   
   
6. The Deep Eyes Squad (Grey, Neil, Ryan and Jane) almost mirrors the Avalanche team from FF7. Ryan is Barret, and Jane is Jessie. (or maybe Tifa?) Apparently the Deep Eyes Squad being made up of four people is a reference to earlier games in the FF series, when you could include four characters in your main party.
   
   
7. Although this has nothing to do with Final Fantasy VII, I'm going to include it anyway: the colours of Gaia and the Phantoms (blue and red respectively) are the same as those of Gaia and Terra in Final Fantasy IX.