To crochet without turning you must continue working with the same side facing you. That means one of three possibilities:
1) You are working in the round to make a doily or another similar pattern that just continues round about a center with ever increasing stitches per round to keep if flat (or less increases to let it curve into a bowl shape like a beanie hat. This can be round, square, pentagonal, hexagon, heptagonal or more sided.
2) You are working in the round on a tube shape like a sleeve, leg, or a cup cozy.
3) You could be working alternating rows from left to right either by using a reverse crochet stitch (which I find difficult to perform) or you could be using your left hand to crochet from left to right.
I think it is far easier to turn at least part of your work. One need not turn the entire Afghan but just enough to let you work the working row be turned. When the length is long enough the cast on row is far enough away from the working row to let you twist the blanket in the middle. Then the next turn you untwist the middle rows.
There are patterns for circular blankets or afghans, but you would still need to move the entire afghan (like turning a Lazy-Susan) to work all around the edge in each round.
Actually, a bowl large enough to hold most of afghan placed on a Lazy-Susan could help in turning you work, but I'm not sure that is an answer that you were looking for. [/COLOR]