HAVE TO: OBLIGATION (LAW/RULE)
You have to show your passport at the UK border.
DON'T HAVE TO: NO NECESSITY
You don't have to pay for your food on this flight.
NEED TO: OBLIGATION (important, but not law/rule)
You need to keep your passport in a safe place.
NEEDN'T + VERB: NO NECESSITY
You needn't take an umbrella - it won't rain!
SHOULD + VERB: ADVICE
You should arrive at the airport early.