An erection happens when blood is pumped into the penis - and stays there - making it stiff and hard. It is a complex process, involving the blood vessels to and within the penis as well as the nervous system that controls the flow of blood and, on top of it all, the man’s emotional state. Many sorts of influences can therefore stop erections from occurring.

Psychological causes
Anxiety about 'performance' will almost certainly make it difficult or impossible to get an erection.
Problems in a relationship may affect potency.
Impotence may be caused by depression.
Bereavement: recent loss of a loved one is notorious for causing impotence.
Tiredness.
Stress.
Hang-ups - for instance, guilt about sex.
Unresolved gay feelings.

Physical causes
Problems with the chemical mechanism that makes erections happen - very common in older men.
Vascular (blood vessel) disorders. Patients with arteriosclerosis, other heart or vascular diseases and high blood pressure are at greater risk of developing impotence.
Excessive drainage of blood from the penis through the veins (venous leak) – uncommon.
Diabetes often creates erection difficulties.
Smoking increases the risk of developing arteriosclerosis and, therefore, of suffering from impotence.
Side effects from certain drugs, such as some blood pressure (BP) treatments, some antidepressants and some ulcer healing drugs; antidepressants and BP drugs, in particular, do this very frequently.
Side effects of non-prescribed drugs (tobacco, alcohol, cocaine and others).
Nervous system diseases - uncommon.
Major surgery, eg prostate surgery or other abdominal operations.
Hormonal abnormalities - rare.