The factors that determine the price elasticity of demand for a good are:
substitute goods - if a good has many substitutes, a change in its price will have a major impact on its demand. Consumers will turn to the substitute goods instead of buying a good that suddenly has become more expensive. A good that has many substitutes thus also has a high price elasticity of demand.
proportion of income - the larger proportion of income a good constitutes, the more responsive its consumers will be to changes in price. If a good only constitutes a small proportion of a consumer's income, the demand for the good is likely to be price inelastic.
luxury or necessity - if a good is a necessity (eg. food), consumers will continue to buy it regardless of changes in price. If a good is a luxury good, an increase in price might cause consumers to stop buying the good. Thus, the demand for luxury goods tends to be price elastic, while the demand for necessity goods is price inelastic.
addictive or not - much like necessity goods, if a good is addictive (eg. cigarettes), consumers will continue to buy it despite changes in price - its demand is price inelastic. If a good is not addictive, consumers will be more responsibe to changes in its price.
time to respond - in the long term, the demand for most goods is price elastic. This is because over time, consumers can find (cheaper) substitute goods and quit addictions - in the short time they cannot. If a change in price is only temporary, costumers are unlikely to bother doing this. Hence, in the short term, demand is rather price inelastic.
The factors affecting price elasticity of demand can be remembered using the mnemonic SPLAT.