Some other styles

One way to make your strumming more interesting is to pick some of the bass notes of the chords individually and then hit the chord, as the picture below:

This style is known as pick'n'strum. The bass note is usually the root note of the chord. Here is a well-known chord sequence that lends itself to this approach.

For this picture below,

the bass notes are not all root notes, though the technique is the same. Introductions to songs and links between choruses and verses sometimes feature a phrase played in single notes, wit chords in between, like:

A song like Wish You Were Here by Pink Floyd or the intro to Led Zeppelin's Over The Hills And Far Away are examples of this popular approach to pick'n'strum.

Materials are from the book Guitar.