The most common kind was granny square blankets in a single neutral color. For my second baby I wanted to make him his own granny square blanket. I wanted more color than my grandmothers so I modified the traditional sunburst square to have larger spots.
This makes a beautiful baby blanket, using only knitting (no purl stitches!). The secret is that every seven rows you change to different needles--using one large set and one small set. I've made several of these.