Note that I only provide an overview of a few rumors here, because I'm lazy. If you want to read about more in depth, check out The Final Fantasy VII Citadel or The Turk Alliance.
Aeris's Resurrection
Optional Characters
WEAPON Summoning
Holy and Black Materia
Taking advantage of the stupidity, a guy named Ben Lansing decided to make up a way to resurrect her, just to see exactly how stupid people were. That post can be read here at the Final Fantasy VII Citadel.
A lot of people bought the story - hook, line, and sinker. Pure wishful thinking, if you ask me. Lansing's bullshit escalated into a full-blown video game urban legend (aided along the way by Lansing himself and a few friends), and stayed that way until some time after the game came out in the US. Then, after a long absence from the web, Lansing finally caught wind of what his story had turned into. Somewhat amused, he posted a confession online.
There are even alternate ways to bring Aeris to life that (as far as I know) sprung up after the Ben Lansing original (such as the method mentioned in the Holy and Black Materia section) and rumors on events that happen after resurrecting her.
If you somehow manage to resurrect Aeris, another rumor says that Jenova Rebirth is supposed to appear. Jenova Rebirth is supposedly the most powerful form of Jenova.
Just about every FF7 fan out there knows the story by now, but the sane ones know now that it's complete bullshit.
None of these rumors really sound valid at all. In fact, a lot of them are really laughable. One of the supposed methods for recruiting Sephiroth, for example, is to collect all of the 1/35 Soldiers in Junon; then, he'll show up and say that you have
Some rumors say you can obtain Joe if you beat him and his black chocobo in a race several times, or that you can obtain Dio if you win enough at the Battle Arena and then fight Dio. One even says that you can get the Super Sweeper on your team if you obtain one at the Gold Saucer and then have Shera fix it for you. You can even get Mr. Dolphin if you beat Emerald WEAPON and have 99 Elixers afterwards, according to the bullshitters.
*Excuse me; I mean action figures, of course.
There is supposedly a way to obtain materia which allows you to summon WEAPON. To get it, you have to defeat any of the WEAPONs (except Diamond), and once they lose half of their HP, you can use only a mastered Morph materia and a Luck Plus materia. Afterwards, you'll get an emerald, ruby, or zircon gem. With one of these, you can get a WEAPON materia at Cosmo Canyon.
These summons are said to deal three times the damage that Knights of the Round causes, as well as giving your enemies various effects (which doesn't really matter, because who the hell could survive something three times as strong as Knights of the Round besides bosses? And bosses are almost always immune to status effects, so that doesn't matter anyway).
The drawback is that they'll cause damage to your party as well. The only way you can survive the attack with a Final Attack materia combined with the Phoenix summon.
I don't know the method to obtaining the Black Materia, but once you have it, it'll supposedly raise all of your states to max - except Luck, which will head straight down to zero. It also lets you use the Meteor spell, which is said to be more powerful than Knights of the Round.