Rembrandt was the first person to do these two things:
Paint art for arts sake (and not a rich person or the pope, ect)
Paint interesting group paintings.
Look at The Night Watch for example. Not everyone is completely visible. He experimented as opposed to his early Dutch Masters painting.
So he went on to inspire people like Jacque Louis David and JMW whistler. He inspired a lot of Romantic painters that came after him.
Rembrandt is also the greatest biblical illustrator so you could say he inspired any other related bibical illustrators.