For airline tickets, you can get free passage to certain destinations! Just claim you are on a mission from Allah. This will get you a one way free ticket to a secret CIA torture prison.
When at the grocery store (or a retail store), have a friend cause a disturbance in eisle 7 while you switch the 0 and 9 buttons on the cash register (note: this method will only give discount on items with prices such as 4.99, 2.99, etc.)
Go old school. Adopt a senior look at claim to get a 65+ discount.
Iterate loudly prices of goods you wish to by, followed intermitantly by the word "preposterous".
Talk loudly about the price at the other store of the item you wish to buy.
Pose as a agent from the inspection agency. Talk about the poor quality of the products, and the new quality requirements and standards which are not being met.
Pose as an agent for the landlord of the building. Say that the establishment has ten days to sell everything because they have to tear the establishment down to make way for a luxury apartment building.
If you wish to then buy a luxury apartment, make friends with some homeless people. Invite them to live down on the streets by the desired real estate. Or better, to try and frequent in and out of the building, making use of washrooms, bothering residents, etc.
If you're at a Grocery store yet again, claim that you are Aunt Jemima's 4th cousin and that if only she was alive she'd be making you those pancakes. Then start weeping for her long lost soul, making wild gestures and crying "Oh Lord, if I could only taste her delicious pancakes one more time!"
Claim you are Mother Teresa's great nephew/niece, and that you rely on other's generosity to continue her great work.