Years ago I've read about a young man you had lost a large section of his brain (frontal lobe) in an accident but surprisingly he survived it and continued his normal life. You may have read about that.
Now let's break down the question into 3 steps. Which parts of the brain can we remove without:
- Affecting the normal life. This means, still being able to see, talk, understand, and more. Just like a normal person.
- Losing conscious. This includes just being able to maintain conscious, being able to think and understand.
- Dying. Which means only having the crucial organs such as heart and lungs running.
UPDATE
I'm neither looking for a list of every part of brain's million sections, nor it's possible to cover them all in a single answer. I'm merely looking for a list of widely-known largely-scaled sectioned, such as the below image.
Image credits goes to Mid Brain Power.