Did you know that most regular sewing machines have a special overlock stitch that mimics a serger's stitch? It's true! My Bernina has one, and so have the Pfaff and Brother machines I've sewn on.
Most people without a serger use pinking or zigzagging to finish their edges, sometimes without even knowing they have an overlock stitch on their sewing machines. What makes this stitch different from a zigzag is that it has a special foot with a little pin that helps the stitch wrap around the raw edge of the fabric. It uses more thread and can be pretty slow-going, but it's very secure.
Here's the top view of the stitch on my Bernina 1008, in pink thread. The bobbin thread is yellow.
Since my serger needs to go to the shop, I used my overlock stitch to finish the raw edges of some fabric before pre-shrinking it in the dryer. The overlocked edge held up just as beautifully as a serged edge does!
Do you use an overlock stitch?