Monkeys are cute, and you might feel the urge to play with them, but it's not the best idea. These are wild animals and they can be aggressive, especially if they want to take your food. Be careful while crossing Ram Jhula and Laxman Jhula bridges, the monkeys often rob people of their fruits there. Put your food in non-transparent bags while walking in Rishikesh, or at least cover it with your shawl. Do not try to play with monkeys and don’t smile to them. They perceive eye contact and display of teeth as a sign of aggressiveness. Do not try to approach baby monkeys as their mothers might become aggressive.
Though gray monkeys (hanuman lemurs) are considered to be more aggressive than red macaques, I have seen quite aggressive behaviors of lemur gang on the trail to Nilkanth. Do not leave the door of windows of your room open, otherwise, monkeys will come and check your stuff. If you do get bitten by a monkey, even lightly - to the degree that your skin was cut and you see blood - you will have to go to the hospital and get rabies shots, unfortunately.