Cardio makes your heart, blood and respiratory systems strong - it also makes you lean. In my humble opinion (I'm just a poorly informed fitness n00b), cardio is the most important exercise for long term health and for weightloss.
Having said that, strength training is great for enhancing your strength, looks, and metabolism. Strength training can help you maintain weightloss long after you finish cutting calories.
The more that I read about the issues of how to divide cardio and strength training, how often to workout, how often to exercise muscle groups, etc etc - the more that I feel that you should read as much as you can, take in as much advice as you can find - then design an exercise regime based on what you actually enjoy doing!
I enjoy cross-country running with my dog, but right at the moment I enjoy strength training more. I workout in the gym 3 to 4 times per week, each session lasting 45 to 100 minutes long. A short cardio warm up, then onto the free weights / machines for an hour. I usually try to hit most of my major muscle groups, but I try also for variety. Bench presses (dumbbells and smith), lat pulls, pull ups I do as a staple. I try to have a rest day in between workout days. I used to run on these rest days, but now I try not to run more than once per week - keeping my energy for the strength training. Every few weeks or so I have a three day bonanza - specialising on different muscle groups for three days without a rest day.
The dog? Well, on top of the weekly run, he also makes sure that I walk a few miles extra every day.
I don't mix too much cardio and strength training together on one day - but horses for courses, whatever suits you.
I would recommend more cardio to people who are actively aiming to lose weight. As corndoggy suggests - there are a lot of different cardio exercises and props. When I cut next - I will reduce the strength training programme to spare more energy for the running and cardio workouts, but I would recommend some regular strength training to weight-losers, in order to preserve and enhance that metabolism.