The most common chord progression

I feel like this one should be taught first, and then people can learn other ones.  

I - IV - V - vi

To explain how this works, let's look at two examples:

Key of D

D (I), G (IV), A (V), Bm (vi)

Key of G

G (I), C (IV), D (V), Em (vi). 

Note: m means minor.

Does anyone see the patterns with these keys?