I've made many plastic bag tote bags over the years. They're strong and sturdy, and they last for a really long time (I'm still actually using the first one I ever made), but plastic bags come in all colors, and I have fun making multiple totes to fit my moods.
They're strong enough to carry a LOT of things, even when they're not lined. But I quickly discovered that they're sometimes too good at stretching to carry a bigger load. When I'm carrying books or other heavy materials, the bags sometimes stretch too much. A lightweight (non-stretchy) lining fabric fixes the problem easily!
Now, I line almost all of my tote bags. Here are some of my favorites.