Hi there,
You definately don't want to work the same muscle groups everyday. When you lift weights your muscles tear and break down. They need about 48 hour to "recover" and grow. If you worked the same muscle group the next day you would tear them more and they would never heal and grow.
Your body does need REST and recovery. It doesn't mean that you can't work out everyday, but I wouldn't lift weights even alternating every day. I try to alternate cardio in between weight lifting to give my muscles time to heal. Some weeks I do work out 6-8 days in a row, but when I feel tired, fatigued etc I rest. This week I overdid it on Sunday so I took Monday and Tuesday off and didn't do anything (cardio) till last night. You must listen to it. Overtraining can cause you to be irritable, tired, moody, depressed etc. If you listen to your body it will tell you when you need rest and you can adjust accordingly.
I fight not wanting to rest every week. I hate to rest when I feel good exercising, so what works for me is to watch my body and rest when I feel I need it. Trust me, my body tells me!!
If it were me, I would stick with the every other day / with cardio in between and move up to higher weights and maybe longer or more strenous cardio to kick it up.
The book that Molli mentions, Body for Life is very interesting. He alternates like this (this is taken from his website Body for life)
Day 1 Upper Body Training Chest/Shoulders/Triceps/Back/Biceps
Day 2 Cardiovascular Workout
Day 3 Lower Body and Abs Training Quads/Hamstrings/Calves/Abdominals
Day 4 Cardiovascular Workout
Day 5 Upper Body Training Chest/Shoulders/Triceps/Back/Biceps
Day 6 Cardiovascular Workout
Day 7 Rest
Don't be afraid to play around with your exercise schedule and find what works best for you. Good luck!