Around two or three months ago I changed the position of the side mirrors on our car.
article in Car and Driver which was linked by lifehacker. Check it out - it has completely changed my driving experience. I drive in rush hour and in NYC traffic every day, and being able to see my (former) "blind spot" without twisting is an absolute joy. If I look in the rearview mirror I see what's behind me, and when I look in the side mirrors I see what's next to me. Once a passing car leaves the side mirror's view it's in full, normal, forward-facing view.
I suggest that if you try this, at the beginning continue to check your blind spot as you normally would until you get used to the new view. You'll naturally gradually stop that check as you get comfortable.
One caveat, though, parking is more difficult, since you can't actually see the side of your car anymore. You'll need to lean to get that view in the mirror. But, in my opinion, it's well worth it for far safer driving the rest of the time.