I'd say it largely depends on the story.
I am currently in the process of watching the TV series, Lost. I will say this: The characters are round and dynamic.
Is this important to the story? Absolutely.
Why? Because it clues us in to two major things: 1) why each acts and thinks the way they do. 2) it may be a reason/clue as to why they are there to begin with.
Backstory is vital to character development.
Possibly the most developed character I personally have ever written is Gatorverne McLeod. She is one of my supporting characters in Catching the Sun. She continues to surprise my readers as I continue her story.
I think of Flashpoint when I think of very round and dynamic characters. I think of Ed and Sam and Jules when I think of a past that brought them to where they are. I think of Greg when I think of a character who has overcome so much and has been through so much. When pressure is high I think mostly of Spike, who never lost his cool until it was all over.
And there is a reason for each and every characteristic and flaw in each and every one of those characters. And it all comes from their past.
We are who we are today because of something that happened yesterday. Either we did something right or wrong or did nothing, and it could have been so much different, but it isn't. We don't notice things like that; neither should our characters. But we should most definitely consider, as the writers, what could have been.
I am most attracted to characters who have problems in their past. The trials they face and overcome mean so much to me; it shows just how much I, as a reader, can overcome if I put my own mind to it. It also shows that some people don't "get over" it. I think of Ed Lane and Sam Braddock (from Flashpoint) in particular, who clearly still deal with what they caused to happen. They struggle internally, and it shows through in the form of actions.
Our words and actions always, always result in reactions. Shouldn't it be the same with our characters? Everything they say should result in something being said or done by another character. Everything they do and say should reflect something else.
Nothing without purpose. Why did that character die? Why didn't that one? Why did she torture them? Why did he ignore her. Why did he fall in love with her? Why didn't she fall for him?
Everything happens for a reason, and you need to know that reason. This is why history is important.
Keep it up!