A zig-zag stitch is useful for when you need to sew a stretchable seam (like when using knits). You can also use it for a decorative effect, or to lock the edge of your fabric.
As most, if not all, sewing machines can sew a zig-zag stitch, it’s a popular alternative for when more specialised stitches are not available.
Everyone’s favourite encyclopedia has more on the zig-zag stitch: Zigzag stitch on Wikipedia
Picture by Kristin Roach