Theories concerning the Animagus-transformation
While collecting the Animagus-stories for my list, I've read all kinds of stories with very diverse ideas of how to become an Animagus. Most of the stories don't fit my personal idea of the Animagus-transformation.
Some of the stories allow for multiple forms. With the exception of one single story where the two forms stem from the fact that Harry and Ginny share a soulbond and thus can share magic and each other's form, I don't really believe that multiple Animagus-forms lies within what JKR intended.
Many stories have magical forms. In particular I have now read 12 stories where Harry becomes a phoenix and know of one more where he likely will be one once he studies the transformation. This is another thing that certainly doesn't follow canon (nor my own personal perception of Animagi).
The next thing: how to actually become an Animagus.
There are quite a few stories out there, for example Dark Phoenix, Peorth and more, where Harry becomes an Animagus from one moment to the next. He neither studies for his transformation nor wills it another way. Just from one moment to the next, he changes. How likely is this, considering how JKR describes Animagi? In canon becoming an Animagus is hard work and few even try it as it just takes so much work.
Then there's the next thing: choice. Many writers describe it as "pick an animal you are familiar with and concentrate on it till you change". If Peter Pettigrew had had a choice (and had had to pick an animal he was familiar with), do you truly think he would have become a rat? JKR describes becoming an Animagus more as finding your own inner self, the one animal that you relate to most. I vaguely recall a quote that one of the reasons why only a select few ever tried the transformation is the very fact that you can't choose: why go to all the trouble if possibly you might just end up as a cockroach?
As for McGonagall teaching it at school, considering that there are only seven registered Animagi in the 20th century, how likely do you really think this is?
Some other writers write about something like Animagus-potential. While this would explain why there are so few out there, isn't it a huge coincidence that all three Marauders who tried it actually had the potential?
(The fact that lycanthropes or metamorphs can't become Animagi as some authors have stated of course does make sense.)
What you do need, however, is some skill, aptitude and dedication. (As described in canon Sirius Black and James Potter had all three. As for Peter Pettigrew he was greatly lacking in skill and aptitude. He only managed the transformation with lots of help from his friends.)
We know that there are only 7 registered Animagi and we already know of 4 unregistered Animagi. Considering the amount of Animagus-stories out there, the amount of unregistered Animagi would have to be 100 unregistered Animagi for every registered one. :p
Well, now, what do I actually think?
1) Neither magical nor multiple Animagi are possible (no, not even if you are Harry Potter, Chosen of Prophecy, and whatnot. Not even if you win Witch Weekly's Most Charming Smile more often than Lockhart! :p)
2) Becoming an Animagus isn't easy. It's hard work. As stated above you need skill, aptitude and dedication. The one story I've read which really illustrated that very well is Harry Potter and Dumbledore's Army by CatCalls. That's the one story which features Animagi in a major way that I really can recommand. The author explains very well what makes the transformation so hard: you not only need to be able to cast silent, you also need to be able to cast wandlessly. (How else would you get back to your human shape otherwise?)
Oh, and one particular pet peeve for all you writers out there who use Animagi in your stories: Animagus is the singular and Animagi is the plural, get it?! It simply pisses me off how many people have not the least idea about what they are writing about!