"I'm working on some acrylics on stretched canvas, which I'm not planning on having framed (at least, not any time soon). What should I do with the white edges (the sides of canvas covering the frame)? I was thinking about painting them a solid color, such as black. What do you think?"
There is no rule when it comes to dealing with the edges of a canvas. It's a matter of personal preference. If you're planning to hang a canvas unframed with the sides showing, consider painting the edges in a color that was used in painting itself. Leaving the edges white makes them stand out too much, as does painting them black (unless the painting is dominated by dark colors).
Some people continue the painting onto the sides, 'around the corner' as it were, sometimes in as much detail as on the front of the canvas. Personally, I think it's enough to just paint a single color (or perhaps two).
When I'm painting I try to remember to do the edges at the same time as the initial blocking-in of shapes. That way I don't have to be extremely careful when I do it and stress about having paint dribble over the edge onto the finished painting. It's also a way to 'use up' excess paint on a brush when I'm about to swap over to another color. Then when I've finished the painting, I touch up the edges carefully if needed.