It is certainly safe to train all muscle groups on the same day. I personally recommend working each muscle group at least twice but no more than 3 days per week, with at least one rest day in between working any specific muscle group. Thus if you complete a full body routine every workout day, you wouldn’t want to weight train more than 3 days total per week with a rest day in between each workout.
If however, you want to train with weights more often then 3 days per week you could complete a split routine (such as lower body one day, upper body the next; or dividing it further into muscle groups, etc).
Personally I like completing 1 upper body, 1 lower body, and 1-2 full body routines each week; the second full body routine an easy day for trying new exercises or having a light workout day. An example schedule would be:
Monday – Upper Body
Tuesday – Lower Body
Thursday – Full Body (heavy day)
Saturday – Full Body (light day)
This is only one example; you would want to experiment with what works best with your schedule and your body. There are an infinite number of ways to divide your workouts; here’s a blog I wrote with many examples: http://www.integratedfit.org/webblog/?p=36. Rest between the workouts is just as important as the workouts themselves; so remember that it’s not just about the days you train, but the days you train well.