Some apples are self-fertile, which simply means they can produce fruit without a pollination partner (a companion apple tree). However, most apple cultivars need a companion tree close by to provide cross-pollination to ensure good fruit and higher yields.  As a general rule good cross-pollination occurs between apple varieties that flower and fruit around the same time.   

The chart shows recommended pollination partners, however in most cases you can choose another apple which ripens around the same time.  

Triploid Apples are the exception to the rule as they carry an extra set of chromosomes (3 rather than 2) and they require 2 pollination partners as per the chart below.

Ripening times are a general guide, provided by growers - Early = Feb-March, Mid = March-April, Late = April-May.