The Law of Demand states that as prices increase, demand will decrease, and vice versa. That is to say, price and quantity are inversely related.
There are some things which have an inelastic demand, meaning the quantity demanded will remain constant no matter the price. Medicine is a good example. Vices to which people are addicted are as well, so some degree, and tobacco stocks are considered fairly safe and defensive in bad economic times.
The demand curve can shift one way or the other if it is influenced by factors outside of the demand curve parameters (price and quantity).