The primary problem, and (pardon the pun) the most pressing one, is population. As life has evolved, the prime directive has been to make more. The Hand which designed each creature didn't install a governor; things fit together so that pressures from outside took care of restricting populations--shortages of food, adverse climates, fires and floods, and predation all played a part.
So things remained in almost steady state for millenia. As recently as the early 1800s, interested trackers of world human population growth asserted that the rate was constant, and, projecting to the future, claimed that it could continue unchecked for a very long time without significantly filling up the earth.
In 1798, The Rev. Thomas Malthus, a near-contemporary of Charles Darwin, proposed the theory that population actually grew exponentially, rather than arithmetically (food production, he said, only grew arithmetically). That is, instead of increasing by the same number of people every year, he said the population would continually double in a fixed period of time. He suggested that in situations where there was no restraint, the doubling period was around 25 years. In fact, from a population near one billion in 1800, the doubling time to two billion was about 130 years. From two billion in 1930, the population doubled again by about 1975, to four billion. Eight billion humans are expected by about 2015.
...so Malthus appears not only to have been right, but too conservative--population has grown much faster than exponentially.
Just what is the maximum the Earth can hold? Estimates tend to cluster between 8 and 25 billion. At current doubling times we will reach the high end of this range by the end of the 21st century.
The question is not whether population growth will stop, but whether it'll stop because of resource shortages and environmental damage, or because Humans confront the problem and choose to stop it.
Want more? Visit The KZPG Overpopulation Reduction Home page or Joel Cohen, author of the recently published How Many People Can the World Support?