Endurance and strength are the foundations of a good fitness plan and good health in general. One should not be ignored in pursuit of the other for long periods of time.
If you are training for an endurance event, you need a specific program that will gradually increase your intensity and volume over time. Establishing a base in your particular sport is of utmost importance so get your miles and time in, there is no substitute. A solid strength base will only improve your performance.
For general cardiovascular endurance, a moderate intensity workout for 30-60 minutes 3-5 times per week is good for your overall health and will mitigate the majority of health problems associated with inactivity (not obesity). This can be walking, jogging, rowing, running on an elliptical, swimming, or simply leading an active lifestyle.
Interval training and high intensity interval training can be used to enhance your baseline endurance, but without a broad base, your gains will be minimal. Train for short periods of time and you will only be good for short periods of time.