First of all, it depends on the deck type and your hero choice. Warlock's hero power has built in card draw that eliminates much of the need for card draw mechanics on cards. If you are playing a slower late game deck, you might be able to get away with slightly less card draw as your hand will be filling up naturally.
Card advantage is extremely important to win in Hearthstone. If you run out of cards, you are limited to playing only what you randomly draw that turn, rather than picking the best card from your hand. This severely limits your options to deal with your opponent.
Watch how many cards you play each turn, every turn. Each time you play more than one card in a turn, and only replace them with the single draw, you are losing card advantage. The more mana you have, the more cards you will be able to play each turn. Note which turn you run out of cards (or have nothing valid to play). Also note how many cards your opponents have on these same turns.
Then increase the amount of card draw in your deck until you can keep up with the pace of the game.
Finally, cards that perform an action/summon a creature and draw a single card (also referred to as card cycling) are not the only answer - more efficient card draw mechanics can come from cards such as Northshire Cleric, Gadgetzan Auctioneer, Acolyte of Pain, where more than one card can be drawn from a single card, increasing the value.