Why do different blood types exist?

Answer 1

They exist because of different genetic mutations that have occured throughout the history of human kind.

Answer 2

They aren't there just to make it hard to get a transfusion, that's for sure.
They are proteins that are on the red cell membrane. They vary in their functions, some are adaptations to Malaria (Duffy antigens) some have transport functions across the membrane.
Below is a link to a pdf file that gives a summary and diagram, about 5 pages in (on page number 206).

Answer 3

because they come from different people