This painting combines what we see today as classical with a few things that might be a little more out there, depending on what Michelangelo meant by the painting.
Firstly, we see that everyone is a huge hulking man. Michelangelo for some reason liked to paint huge hulking men. Michelangelo himself was quite muscular (and apparently an asshole) and it seems that artists have a habit of painting themselves into their work.
I don't think that Michelangelo meant himself to be Adam or God in this painting, considering that he probably wasn't thinking about it beyond subconsciously including his physique in both Adam and God. My reasoning for this is that Michelangelo was painting a shitload of other works on the roof of the Sistine Chapel and probably put himself in a few parts of it, but not every single little work.
As we can see, with so many characters, it's hard to assume that Michelangelo conciously put himself as a person into more than a handful of these people/angels. There are repeats of characters though. God, for example, is depicted a few times.
The Jews probably shit themselves when they found out this was going on. For so long they had felt that depicting God in any image whatsoever was not only impossible, but just completely wrong to even attempt, sinful even. The Temple had no paintings or statues in it because the Jews didn't want to make the mistake of worshiping an image rather than God himself.
As an obscure history note, Caligula wanted to put a statue of himself in the Jewish Temple to make sure they were under control. He was eventually convinced that this would put an already fragile region in total chaos.
The early Christians seemed to make this mistake of worshiping the image before God a few times. Whereas the Jews didn't want any images of anything anywhere near their Temple, the Christians couldn't get enough of them. We have paintings, stain glass windows, and statues everywhere. Even the rosary has a little Jesus on it.
Another interesting thing about the painting of the creation of Adam is the shape that surrounds God. It looks like a brain. Some have postulated that Michelangelo might have been theorizing that God was created in the mind of man.
For those of you that haven't heard of the Flying Spaghetti monster, it is basically the incarnation of atheism. The point of FSM is that there is as much proof for God as there is for something as ridiculous as a flying spaghetti monster. The entire idea is a mockery of Christianity in particular, given that Christianity is the religion that most criticizes atheism.
Followers of the Church of FSM claim to have been 'touched by his noodly appendage', a clear mockery of being filled by the Holy Spirit. The concept points out some of the absurdities in the conscious higher power, however it doesn't really apply to the belief of the natural pantheistic subconscious god. Say what you want about the Church of FSM, but the mockery is all done in good humor. It's like drawing a mustache on the Mona Lisa. Some people find it funny.
I don't know what members of the Church of FSM would think about pantheism or other forms of the subconscious god (such as some forms of elemental paganism), but odds are that they wouldn't appreciate it.