Dialogue in Fiction: Does each character need to have his own voice?

Writing advice I see often: make sure each character sounds different from the other characters.

I admit it, I have a great deal of trouble with this. I have a hard time making different characters in my stories have their own unique sound or voice. I'm sure this is a great benefit if you can do it. I'm sure it will make your story more realistic.

You can pull this off more easily if you have characters from distinctly different backgrounds, say a cowboy and an Indian, or different nationalities, say, an American and an Italian. But two Americans talking would be harder to do. I think a lot can be accomplished through dialogue tags, such as "she whispered" or "he shouted" and the use of some italics and the use of some colloquialisms. Of course, some voice can be attained by a character swearing or speaking brutally while another is soft spoken or compliant. A lot of what characters say and how they say it grows out of their personalities, which means you need to have a good understanding of each character's personality.

This being said, I must admit that I have trouble with this and need to work on it harder.

What about you? Do you have a way of giving different characters unique voices? Do you think how they sound is just as important, more important, or less important than what they are saying?