Draw and Play Rules are Rule Cards which state the number of cards to draw and play per turn. Typical numbers include "Draw 1" and "Play 1" at the start of the game, or "Draw to 5" which allows players to play as many cards as they want and then draw cards until they have five. It is not uncommon for people to change these for their convenience- both draw and play limits of 1-7 and their draw-to variants are common. "Play all of the cards in your hand each turn" is also an extremely common variant. There are a number of notable cases in the game which draw some controversy.
Draw Zero, Play Zero
Drawing zero cards per turn is a difficult scenario. Typically, if it is the result of a "draw zero" rule, then the rule is discarded when someone runs out of cards. Otherwise, it could prematurely end the game if not taken care of. Playing zero cards is even more of a problem. If no cards are played, then the game does not progress at all. Usually, in this situation, cards which remove the "play zero" card are allowed to be played. In addition, there is commonly a house rule which prevents the two rules from being played simultaneously.
Draw Negative, Play Negative
In some strange circles, "Draw -1" and "Play -1" are cards that may be played. "Draw -1" is a card that states "Instead of drawing, place a card from your hand face-down on the draw pile". Similarly, "Play -1" usually is "Instead of playing, take a card from anywhere on the table or off the top of the discard pile and place it in your hand." Draw -1 is likely discarded when someone has an empty hand; Play -1 is usually discarded when someone decides to "un-play" it.