If you take up running, cycling or swimming, which are seen as aerobic or ‘cardio’ forms of exercise, you will indeed get fitter over time, but that fitness is mainly specific to that activity. Unless you’re a triathlete, who spends a lot of time training all three disciplines, someone who is extremely fit at cycling is likely to be comparatively worse at running, and vice versa. There is a skill component to these activities that is often overlooked. The body becomes more efficient at the movements involved, taking less energy each time they're 'practiced'.
The VO2 max test is still the gold standard to measure overall fitness. Athletes are wired up to monitoring devices, and push themselves to the absolute limit to see how much oxygen they can process. A study was done back in the 1970’s, where the subjects trained just one leg on an exercise bike for several weeks; the other leg wasn’t trained at all.
When they tested their VO2 max on the bike, the trained legs showed an increase of 23%, but the untrained legs showed no improvement. VO2 max is supposed to represent overall fitness levels, but this study showed that fitness is actually a measure of adaptations in specific muscles.
If you enjoy activities such as running, cycling and swimming, then by all means go for it. However, you must have great technique to minimise the wear and tear on joints and ligaments, and take preventative measures to improve recovery.
If your goal is simply to look and feel better, then prolonged cardio exercise is a waste of time, and you will get far more benefit out of full-body resistance training and regular brisk walks.