Why do people use and abuse drugs?

There are many reasons why people use drugs. Some people use drugs because they like the rush it gives them or because they are thrill-seekers. Others may try a drug out of curiosity or because their friends do it. However, many people use drugs in order to cope with unpleasant emotions and the difficulties of life. In fact, the National Alliance on Mental Illness estimates that around 50% of drug abusers also suffer from a mental illness such as depression, anxiety, bipolar disorder, or schizophrenia.
People who are suffering emotionally use drugs—not in order to get high—but to feel normal. Drug use can be a seemingly attractive and easy escape from all kinds of problems. Speed might be used to fight feelings of inferiority, sleeping pills to deal with panic attacks, or painkillers to numb depression. However while drug use might make a person feel better in the short-term, this attempt to self-medicate ultimately backfires. Instead of treating the underlying problem, drug use simply masks the symptoms. Take the drug away and the problem is still there, whether it be low self-esteem, stress, or an unhappy family life. Furthermore, prolonged drug use eventually brings its own host of problems, including major disruptions to normal, daily functioning. Unfortunately, the psychological, physical, and social consequences of drug abuse and dependence are often worse than the original problem the user was trying to cope with or avoid.
See Helpguide's Dual-Diagnosis for more on co-occuring psychological disorders and substance abuse problems.