A meta-analysis from the 90s (North, McCullagh, and Tran, 1990) actually found that the more participants worked out, the lower their symptoms of depression. They also found that exercise was particularly effective at reducing depression in older adults. Blumenthal et al. (1999) later showed that individuals randomized to an aerobic exercise group were as likely to be partially or fully recovered from their depressive episode as those assigned to a group treated with antidepressants. Interestingly, people in the exercise group were significantly less likely to have relapsed (i.e., had another bout of depression) after 4 months, compared to folks in the antidepressant group. So in the long run, exercise was more effective than antidepressants at treating depression!
And the research looks pretty promising for anxiety as well. Researchers theorize that exercise provides the body with an opportunity to practice managing stress. The body reacts to stress, be it emotional or physical, in similar ways. Much like exposing the body to a small dose of a disease in the form of a vaccine so that it can produce antibodies, exercise is theorized to provide the body with an opportunity to practice managing and recovering from stress.
So what's ideal? The public health recommendation is for 5 days/week of moderate-intensity exercise (e.g. brisk walk) lasting at least 30 minutes, or 3 days/week of intense exercise (jogging) lasting at least 20 minutes. There is significant research to suggest that strength training is as effective as aerobic exercise, particularly for women (for more info, check out this book), though if your aim is to decrease anxiety, cardiovascular activity is considered superior to strength training (Steptoe et al., 1989). Strength training, stretching (such as yoga), and aerobic activity have been shown to be equally effective at reducing symptoms of depression.
So what's realistic? As a gym rat and yoga instructor, this is something I've thought a lot about. I used to be an avid runner who didn't consider anything less than 5 miles to be a workout. I then developed sciatica and had to give it up. When I was first recovering I could only walk on the treadmill. Since I wasn't running, I loaded up several seasons of Six Feet Under to watch while I "wasted my time" walking on the treadmill. Over time though, I found that I actually looked forward to walking. I could do it everyday, instead of needing time in between to recover, and, coupled with a day or two each week of strength training, I felt like I was in the best shape of my life. These days, I hit the elliptical several times a week and do one day of strength training.
If you don't have time to meet the public health recommendations, consider downloading the 7 Scientific Minute Workout app for your smartphone. The app is based on this awesome article in the NY Times. I have several clients who swear by this app and often end up repeating it throughout the day.
If you have absolutely 0 time, consider finding ways to work some exercise into your current routine. Could you take the stairs instead of the elevator? Ride your bike to work one day a week? Do calf raises while cooking dinner, or squats while watching the news? What's one change you could make?