During my first weight loss attempt, I did not exercise at all. (I also gained all the weight back, plus more.)
When I decided again to lose weight, I incorporated exercise right from the beginning. However, I didn't do that much at first. I ran/walked 3 days a week, starting out with only about 10 minutes total and working my way up as my stamina increased. After that I signed up for a Pilates class and so I was doing some strength in addition to cardio (which at that point was a combo of running, elliptical, stationary bike, and stair climber, for about 30 min 3x/wk). After that I started doing some strength after my cardio during my 3 workouts per week. Eventually I added a circuit training class on the 2 days I wasn't already working out, and did that until I hit my goal weight and for a little while after that until I finished school, moved and got a full-time job.
I had some injuries/health issues so I had to lay off the weights for a while. For a while after moving to Indy I workout out 3x/week for 30 mins on an elliptical. Then we joined a gym and I worked out 3-5x/week for 30 mins, usually elliptical/stationary bike and some weights as I was able.
Then we got a dog and couldn't go to the gym after work since we had to come home to take care of him. Around the same time, my health issues were finally resolved, so I started the couch to 5k running program since my knees didn't hurt anymore. I took the dog with me.

Then I decided to train for a triathlon, so I added biking and swimming to the running for a total of working out about 5 days a week for 30-60 minutes each time. After the triathlon, I added a bootcamp class and weight lifting with the New Rules of Lifting for Women book's workout plans.
In any case, right now I do NRLW weight training 2x/week, and cardio (running/swimming/biking) about 2-3x/week (I aim for 3 but sometimes get only 2).
That's probably way more info than you wanted. Suffice to say the first time I lost weight I didn't exercise and I gained it all back (I'm not solely blaming the exercise, I also ate like a pig once I got to my goal weight!). The second time I incorporated exercise from the beginning, and during maintenance if anything I've increased the amount of exercise I do.
As far as calories go, honestly, I have never counted my exercise in my calorie counting. I lose weight when I eat less. If I ate the same amount and just exercised more, I probably wouldn't lose much weight, if any. The reasons I exercise are: (1) I like feeling strong and fit, (2) I get sick of sitting all day at my job, and (3) exercising helps me stay motivated to eat right. If I don't exercise, I eat crap. If I do exercise, I eat well. I can't explain why, that just seems to be the way of it.
So I would say don't pay too much attention to the numbers that the treadmill, elliptical, etc. report for calories. If you want an accurate count of how much you're burning you probably need to get some kind of heart rate monitor (but I don't totally believe in those either since my heart rate is always high). I guess what I want to say is that exercise would still be important even if you burned 0 calories doing it.