It really depends on what your exercise goals are. An ellyptical trainer is good for cardio workouts, losing weight and toning the legs and glutes, but not so good for strength or building flexibility.
If the ellyptical trainer is helping you reach your goals, and you aren't sore the day after using it, there is no reason why you can't use it every day. Many people do, with good results. But if you are just starting out with it, every other day is probably best.