An Emergency:
HELP!!

Task oriented:
Give me that!

Request:
Put your coat away.

Alerting:
Turn your headlights on! (When alerting someone to something they should be doing)

Positive Politeness:    It is usually seen in groups of friends, or where people in the given social situation know each other fairly well. It usually tries to minimize the distance between them by expressing friendliness and solid interest in the hearer's need to be respected (minimize the FTA).

Attend to the hearer:
"You must be hungry, it's a long time since breakfast. How about some lunch?"

Avoid disagreement:
A: " What is she, small?"
B: "Yes, yes, she's small, smallish, um, not really small but certainly not very big."

Assume agreement:
"So when are you coming to see us?"

Hedge opinion:
"You really should sort of try harder."

Negative Politeness:    The main focus for using this strategy is to assume that you may be imposing on the hearer, and intruding on their space. Therefore, these automatically assume that there might be some social distance or awkwardness in the situation.

Be indirect:
"I'm looking for a comb."
In this situation you are hoping that you will not have to ask directly, so as not to impose and take up the hearer's time. Therefore, by using this indirect strategy, you hope they will offer to go find one for you.

Forgiveness:
"You must forgive me but...."

Minimize imposition:
"I just want to ask you if I could use your computer?"

Pluralize the person responsible:
"We forgot to tell you that you needed to by your plane ticket by yesterday."
This takes all responsibility off of only you and onto "we", even if you were the person responsible for telling the hearer when the deadline was to buy the ticket.

Off-Record (indirect):    You are removing yourself from any imposition whatsoever.

Give hints:
"It's cold in here."

Be vague:
"Perhaps someone should have been more responsible."

Be sarcastic, or joking:
"Yeah, he's a real rocket scientist!"