Some people say that the way to improve is to constantly analyze your games. But many do that and yet very few manage to get above a certain level.

Then there is parctice. But even with that there is a good chance that you'll reach a 'personal max' and won't improve any further.

Or is all down to an exceptional brain?

I would love to hear the opinion of everybody, but especially that of top players.

Many do that? Really?

My experience is rather just the opposite.

What makes an exceptional chess player?

1. Prodigies brains are wired for chess.

2. Average player needs:

  a. Obssessive love of the game of chess

  b. Average cognitive ability

  c. An outstanding memory

  d. Extensive training in visualization patterns through a training regimen.

I think the definition of an exceptional player is rather wide and subjective. For some players, it boils down to getting extensive amount of practice. For some prodigies, they are born with it,so they are naturally amazing at chess. For some players, eventhough they are average, yet they don't need to really analyze their games, they just simply remember the tactics used by their opponents and reuse them. 

Pfren, I have to say that I do try to do this, but ultimately, I really don't know how to effectively analyze my own games.

"Find where you went wrong." Is great advice, but if I knew where i went wrong, I wouldn't have ;)

I think that ultimately one needs a certain amount of knowledge about how to analyze a game before one can do it well. And my problem is that I'm not able to find a good "how to" that shows me how to analyse.

Do you know of a good book or video for C players and below that goes into detail around how to effectively analyze?

If you cannot analyze your own games almost from the start then you can be a good chess player but not an exceptional chess player.

Hint if you cannot analyze your own games then try to have a master or above analyze 2 or 3 of your games and from his/her comments you will learn how to analyze your own games to some extent. 

assuming the master explains his analysis...