Apart from running there are many activities that cyclists can get involved with that will aid their overall fitness.
Most cyclists are fit for cycling but can easily get out of breath running up even a short flight of stairs. Whilst cycling keeps you aerobically fit and you can develop an incredibly strong lower body, from the waist upwards, cycling does very little for body maintenance. Hence the need for cyclists to consider, at least during the off-season, alternative forms of developing general fitness instead of just fitness for the bike.
Unlike some, I believe that running is a superb method of gaining overall fitness and because of this I devote an reasonable sized section to the subject. So is a carefully constructed program of weight training, particularly if you use it to develop strength and endurance in your upper body. Many I know turn to football, squash or badminton. One I know turns to roller blading.
Here are four activities you may feel like trying that in their own way will contribute to an overall feeling of well being and overall fitness.
Running
Aerobics
Swimming
Circuit training