Lifting heavy weights. Everything else you might do depends on strength, so if you don't have that, you'll be limited. If you do have it, everything will improve for you. You'll be more flexible, have better endurance, will be less injury prone and will recover from injuries faster.
It's also very sustainable. You can do one short, high intensity lifting routine per week, not have any significant (or any at all) soreness the following days and make gains (or, once you start hitting the peak of your potential, sustain them). 5 minutes, to do one set of squats or deadlifts, one set of presses and one set of pull ups with sufficient weight to keep you under 10 reps will keep you going, and it's something you'll be able to fit in, even with a changing schedule. Not included in the one set is doing 1-2 warmup sets of 5 reps with lower weights. The best thing is, within a half an hour cooldown after the set you'll still be in shape to do any physical activity that's necessary for your life, and you won't have worn out your muscles that you couldn't move furniture for the next two days.
Obviously there will be some scenarios in which a weight room just isn't available, but there really isn't anything else that could make up the core of your program that can adjust to the changes in life. There's bodyweight routines and rope skipping, but those end up taking a lot more time, which makes them a lot harder to sustain over weeks or months (unless you're doing handstand pushups).
The other answer is walking. 30 minutes per day (or at least 3x/week). That has been shown repeatedly to significantly reduce the risk of most illnesses, compared to being completely sedentary. I have a hard time calling that a fitness routine though, it's really more of a bare minimum. I can't really think of a scenario in which 30 minutes of walking isn't possible.