[subject] + 要 + [noun] [subject] + 要 + [verb] + [object] 不要 + [verb] [subject] + 不想 + [verb]
要 covers wanting something and intending to do it. Before a noun it means "want"; before a verb it means "want to" or "am going to".
Before a noun, 不要 turns something down: "I don't want it".
Before a verb, 不要 is usually heard as "don't", a prohibition. To say you don't want to or don't plan to do something, use bù xiǎng不想 or bù不dǎ suàn打算.
我不要去 is not wrong, but it is a flat refusal – "I won't go!" – rather than a statement of what you want.
These go beyond wanting and intending.
要 can state a requirement with no sense of wanting.
要 can also say what is going to happen.
With 了 at the end, 要 says the event is imminent.