what's the difference between "important to" and "important for"?

When do we use important for and important to? What's the rule? For example:

It's important to me.

Or

It's important for me.

What's the difference between the two sentences?

Important to signifies a connection to the specified subject (in this case me). Important for denotes importance for a certain cause.

It's important to me! refers to something you value or hold in great esteem.

It's important for me! refers to a cause, e.g. It's important for my health/success etc.

"X is important to Y" where "Y" is a conscious entity denotes that Y values X.

My parents are important to me.

"X is important for Y" denotes that X is something that Y really needs or that Y will be severely affected by not having X. In this case "Y" does not have to be a conscious entity.

Sunlight is important for plant growth.

Water is important for survival.