Aborting a landing attempt is called a "go around", because the pilots usually choose to turn around and try again.
London Heathrow reported 551 go arounds in 2010, which is less than 2 per day and represented 0.24% of the total arrivals.
The topic of go arounds came to light after the Asiana 214 crash at San Francisco International last year. According to this information based on the first 7 months of 2013, go arounds happened on 1.31% of approaches for foreign pilots, but 0.28% for domestic pilots (which is close to the figures reported at Heathrow).
Information from CASA in Australia says there are over 800 per year there, but no accompanying number of arrivals is provided.
Using separate statistics, for domestic and international traffic, there are 702321 domestic flights and 162207 international flights in 2013. If only half of the international flights were landing (the other half departing), this represents 783425 landings. Assuming 850 go arounds per year, that is 0.11% of arrivals in Australia. Being averaged over the whole country could account for the lower percentage. Some causes for go arounds such as conflicting traffic would be less common at less busy airports.
According to a consultant on this story, go arounds occur in 0.20% to 0.33% of landings, which matches the other statistics.
So the numbers show that go arounds are not that common, but they do happen regularly and exactly how often this happens depends on many factors. It is much safer to stop a landing and try again than to continue with an approach that could compromise the safety of the flight.
If the pilots have not established the proper altitude and speed in the approach, they should automatically go around rather than attempt to land. They are also required to go around if they cannot see the runway for visual reference by a certain point. If they do not go around, there may be an investigation, because this can lead to a landing accident, which is far more dangerous and costly than just going around.
By going around, the pilots are hoping that the weather conditions will change enough for the next approach to be safely possible. Low visibility weather like fog can easily change in a short time, so if the conditions are only slightly worse than what is allowed, it may clear up just enough to allow a safe landing.