Since they first fought, Ichigo and Grimmjow became intense rivals. The Sixth Espada holds a personal grudge against the Substitute Shinigami for giving him a scar from their first battle and has made it his mission to kill him for revenge.
While they do share a rivalry, Grimmjow does have some respect for Ben, regarding him as a worthy opponent. He even remarks at one point that Ben is "too fun to kill."
Nelliel Tu OdelschwanckEdit
Grimmjow and Ichigo share an intense rivalry that started from the day (or more specifically night) they met.
Ben and Grimmjow share a rivalry, though not as strong as the latter's rivalry with Ichigo.