I'm so glad you asked.
1. One family favorite is a simple straight set with a solid alternate block. Straight set just means you're not tilitng it on an angle, so there's no need for triangles at the corners. Above is straight set. Below is "on point" note the need for triangles in the corners to make it square again.
2. Nine-patch, set on point with an alternate block like this is called a Simple Irish Chain. Typically the values are reversed and the chain is dark through a light background -- but I'm into traditional not necessarily typical.
This is also a place to add in a third fabric. Here I've laid out several fabrics under my blocks to play with how they would look together. Notice how some fabrics pop out against the block and some harmonize. Which do you like best?
3. Another option is to make more nine-patches with the values reversed. When you put them together it makes a checkerboard pattern. I think you loose the distinctness of the block unless you add a sashing. Like this:
4. Sashing works well with nine patch blocks. I like to use "corner stones" in my sashings (those are the smaller yellow squares). I think it makes a nice echo in the pattern.
5. And there is a type of sashing known as "Tic-Tac-Toe" which uses a three bar stripe and tiny nine-patches.
6. That three bar idea can also be used full sized as an alternate block. Instead of cutting all your 45 inch long three stripe units into rows of blocks for the 9-patch, cut some the size of the finished block. Our samples were made at the 2.5 inch cutting measurement for a 2 inch finished square (6 inch finished block), so the striped block will need to be cut at 6.5 inches.
Which can be used in a frame and cross setting direction like this:
Or a stripey setting like this:
7. Simple pieced blocks as the alternate block in a nine patch quilt make up quickly and easily. Here I've laid out my nine-patch blocke with some half-square triangle blocks of the same size.
Hint: this is what that 45 degree line on the rotary cutting ruler is for.