With a specific size and shape in mind, a crochet purse can be constructed without a pattern.
This purse was crocheted in the round from the bottom upwards. It began with a long chain joined end to end with a slip stitch to form a circle, then rounds and rounds were added until the desired bag height was reached. The bottom of the bag was closed by stitching together on the inside with a whip stitch.
The chained circle in the above picture is the perfect size to create a cell phone cover - for a bag or purse, the chained circle would simply be bigger.