Concept:
Printmaking has been practiced by many famous European artists.
Etching, engraving and other print techniques were used by artists to reproduce images and create original prints.
Step 1: Check Rembrandt.
Rembrandt was a great painter and also a famous etcher.
So, he was a printmaker.
Step 2: Check William Blake.
William Blake was a poet, painter and printmaker.
He used relief etching and illustrated printing methods.
Step 3: Check Goya.
Goya was famous for print series such as:
\[
\text{Los Caprichos}
\]
So, he was also a printmaker.
Step 4: Check Vermeer.
Vermeer is famous mainly as a Dutch painter.
He is not known as a printmaker in the same way as Rembrandt, Blake or Goya.
Step 5: Final conclusion.
Therefore, the artist who was not a printmaker is:
\[
\boxed{\text{Vermeer}}
\]