There will always be people who try to take advantage of others. Such practices can be especially acute during the month of Ramadhan, a time when Muslims are enjoined to be charitable.
Some of the common scams seen around the world include:
People with faked wounds or bandages, or carrying children treated in the same way*, ***, ******. A variation is to have sedated children who look ill or starving*.
People who don't have their bank card or wallet with them and urgently need money because a relative is ill**,****,*****. A variation is for the scammer to ask for money to take a taxi because a relative is killed or injured.
People who pretend to be taken ill; the victim pays their medical bills**.
A family in a car who has run out of money for petrol and 'milk for the baby'***, ******. A variation is a mother with a child who doesn't have the money to get home****. Another variation involves a car with its hood up*****.
People who approach others, saying they do not have the money to perform hajj******.
*Described in India in 2011 here.
**Described in Oman in 2008 here; some of the scams are described in the comments.
***Described in UAE in 2011 here.
****Described in the US in 2012 by Snopes here.
*****Described in the US in by Scambusters here.
******Described in the UAE in 2014 here. It is an offence to beg in the UAE.