As seems to be becoming tradition for the series, Halo 4 will require quite a bit of storage to play. Specifically, Xbox.com notes that players will need "at least an 8GB USB flash drive or an Xbox 360 Hard Drive" in order to play Halo 4's multiplayer mode. Furthermore, the hard drive option is "highly recommended" for those seeking an "optimal" experience.
We've contacted Microsoft to see what differences there will be between each option – and exactly what is meant by the fairly all-encompassing term "multiplayer" – but, in the meantime, one thing is clear: in the off chance that you might want to play some Halo 4 multiplayer, you'll need some storage to do it.
Update: Microsoft has responded to our queries, noting that "Halo 4 will offer an optimal experience if played using a hard drive, but will deliver a visually impressive and immersive gameplay experience whether you use a hard drive or a flash storage device." Furthermore, as to which multiplayer modes require storage: All of them. Specifically, "the multiplayer modes the storage requirement applies to encompass all Xbox Live-enabled modes."