Q:

How much running is enough? 

I am currently trying to establish a schedule of running 3 times a week, for 4km.  This is done in the mornings, just as I wake up and before having any breakfast or coffee, just a small cup of water - this fits in better with my system as any food I consume immediately pre-exercise causes me to feel dizzy. 
Is this good enough for general fitness or am I not trying hard enough?  
I plan on increasing this gradually, specifically the number of times I do it a week so that I reach 5 times a week but so far 3 times a week is really what I have been able to do. 

A:

It all depends on how you feel and what your goals are.  A marathon runner will look at that and laugh and say you're not even close to "general fitness".  I complete couch potato will look at you and be amazed at your determination and work ethic.  It's all relative. 
In my opinion, you shouldn't be aiming for general fitness, you should be aiming to always improve.  You don't want to look at the future and say this is where I want to be, and once I'm there I'm all set.  Always be getting better.  Set goals, and once you achieve those goals...set further goals. 
For example, when I started running last summer, I started at pretty much what you were doing.  3-4 times a week no more than 5k.  My next goal was to make it 6 times a week.  Once I started to do that I wanted to improve my time.  Once I started improving my time, I started to try and increase my distance, and then improve my time at that distance. 
Try not to think about getting in shape relative to people around you.  Think about getting in shape relative to yourself, and what shape you're currently in, and trying to break through that fitness into something better.  Set small goals, but also have larger overarching goals, that way you always have something in your sights to strive for. 
Oh, and as a side note...running is addicting.  It's horrible at first, but once you start improving and it becomes a little easier it's hard to go a day without it. 

A:

The Minimum Amount of Exercise Is A Lot
Running a few times a week is not sufficient for general health and fitness.  Major health science organizations recommend strength training in addition to aerobic work.  For instance, the CDC says that according to the evidence,

Adults need at least:

2 hours and 30 minutes (150 minutes) of moderate-intensity aerobic activity (i.e., brisk walking) every week and
muscle-strengthening activities on 2 or more days a week that work all major muscle groups (legs, hips, back, abdomen, chest, shoulders, and arms). 

(If I may interject here: the recommendation of "brisk walking" has been criticized for being easily subverted into plain walking.  They really mean brisk.  It's got to be moderately intense--a hike, not a stroll.)  Anyway, the CDC's recommendations continue:

OR

1 hour and 15 minutes (75 minutes) of vigorous-intensity aerobic activity (i.e., jogging or running) every week and
muscle-strengthening activities on 2 or more days a week that work all major muscle groups (legs, hips, back, abdomen, chest, shoulders, and arms). 

OR

An equivalent mix of moderate- and vigorous-intensity aerobic activity and
muscle-strengthening activities on 2 or more days a week that work all major muscle groups (legs, hips, back, abdomen, chest, shoulders, and arms). 

Scientists who worked on exercise recommendations for the World Health Organization and the UK government say:

· 30 minutes of moderate exercise a day is still the minimum, but vigorous as opposed to moderate activity [is] recommended
· Combining days of moderate exercise with other days of vigorous exercise is better for you
· Moderate exercise should be in addition to daily activities such as casual walking, shopping or taking out the rubbish
· People should do two weight-training sessions a week

