Are you knitting stripes? If you are knitting no more than a couple rows you can carry it up the side. When you get to the end you twist the yarns by bringing the color you are using under the unwanted color and it'll carry it up neatly.
You may or may not like the effect of the colors up the side with more than one color so give it a try on a swatch.
When asking questions ALWAYS post the name and a link for the pattern if you have it.
Thanks Jan I am actually knitting cotton dishcloths that have really neat patterns and some with stripes. A couple you knit like two rows with white and then you change to lime green. If I cut it each time there are going to be lots of strings to weave in and I think that will look like a mess. Am I making any sense at all?