|Beethoven: Bipolar disorder with psychotic features|
|Pink Floyd's Syd Barrett: Schizophrenia|
|Sylvia Plath: Bipolar disorder|
|Ernest Hemingway: Depression|
To a large extent, what's "normal" is a purely social construction. It's just what most people think is appropriate. Every culture and subculture is different. So does being "weird" or "marching to the beat of your own drummer" equal mental illness?
On the one hand, I don't think it's that helpful to think of it that way. Here's how I think about mental illness:
You can be weird and still function. You can be a slave to your muse and still have relatively good hygeine and maintain normal relationships and get out of bed in the morning. When you can't--when you really, really can't keep up with usual tasks of daily living--then it's likely you have a problem.
Mental illness makes it hard to function. Quirks and creativity in and of themselves do not constitute a mental disorder.