[q=Kawaii Ryűkishi]This obviously has some intense deeper meaning that only people who like to show off their sprawling vocabularies intellectuals will be able to perceive!![/q]Damn straight. Here goes...
Numerology has never appealed to me, so I'm not gonna comment on the 'significance' of 7 too much. Besides its status as a 'lucky number' for some, I don't know too much about it. It IS clear, though, that the number 7 (and to a lesser degree, 9) appears throughout the game.
In response to 'Kishi's statement, AVALANCHE actually bombs two reactors, leaving a total of 6.

Anyway, there are some good articles on other websites, detailing this and many other mysterious references in FFVII - in particular, the ever-popular Kabbalist/Qabalist symbolism.

This is a good one:
http://www.geocities.com/anguipes/upd.html

This one has a big list of 'sevens' from the game, most of which have already been mentioned:
http://www.geocities.com/TimesSquare...ff7sevens.html

Really, there's not too much 'significance' to the repetition of '7' in the game; if anything, it's more of an in-joke, or even a coincidence. There's some scope for discussion of 7 as a lucky number, though, especially considering the importance of chance encounters (Cloud and Aeris on the streets, that sort of thing) and BAD luck in the story.

But as I said, numerology's really not my sort of thing. Maybe Besimudo will have something useful to add?