As stated before, virtually any substance that has a substantial enough effect on the body, and needs to be used often enough for it to become habitual can becoming an addiction. It doesn't help that pain relief medication has a history for being used as a means of “getting a fix.” Substances such as morphine and opium have been used to help people fight pain for centuries, and both have been recognized as dangerous, addictive substances. Some opium-based substances, such as heroin, have also been used by addicts in recent years, usually as a substitute whenever opium or morphine is unavailable. The infamous illegal substance cocaine can also be used as pain relief medication, though how much of this is retained in crack after being diluted can vary from sample to sample.
However, addiction should not be mistaken for tolerance. Tolerance occurs when the body adapts to the continued presence of a drug within the system. While this may or may not occur to all people who use a certain drug, there is a chance that anyone can develop it. Basically, a tolerant body has adapted to the effects of a given drug at a given dose, thus negating the effects of said drug. For pain relief medication, this means that it can no longer numb the pain as effectively as before. In such cases, typically with the approval and instructions of a medical professional, the dosage can be increased to achieve the same effect as before the tolerance developed.
Opioids, above other sorts of pain killers, tend to be among the most addictive of substances. Opium is widely considered to be the most potent, concentrated form of this drug, with the medically-restricted morphine being a close second. Another derivative that is medically-restricted is heroin, though it is less likely to be used by a hospital than morphine. The more diluted, commercially-used forms include substances such as codeine, fentanyl, oxycodone, meperidine, and propoxyphene.
As with any other addiction, anyone can be considered at risk of pain relief drug addiction once exposed. However, according to some recent findings, addiction may also have some genetic triggers, such that if one's parents or close family have been addicts, one's risk of addiction in considered to be higher. Conditions such as depression can also increase a person's risk of developing a dependence or addiction to a given substance. However, note that long-term use of medication does not automatically lead to addiction and vice-versa.