<< I was referring to both, actually. Whether someone's 'addictive personality' comes from his/her genes or is learned, my point is that the addiction is the person, not the drug >>
Actually, it is both, more or less, depending upon the individual and the substance.
You have to keep in mind that everything is controlled on a chemical level. Our urges, desires, thoughts, reactions, and inhibitions are chemical. When you get hungry, you have an urge to eat. When you get thirsty, you have an urge to drink, and those are chemical messengers stimulating certain areas of the brain that send us strong signals to react in some way. That's how the brain works.
All addictive drugs manipulate the dopaminergic system, that is they cause dopamine to be released or increase its concentration by blocking its re-uptake. Dopamine is a very important "feel good" neurotransmitter (chemical) that is part of our natural system of reward/pleasure/reinforcement. The more dopamine that is released or the longer it persists, the "better" you feel, to a point.
The classic reward/pleasure/reinforcement area of the brain that is associated with clinical dependence is the nucleus accumbens shell. Drugs which affect an increase of dopamine in this area are highly addictive. Drugs like heroin and amphetamines cause a large increase of dopamine levels that is far greater than what the brain would normally get through 'natural' pleasure/reward stimulus.
If the key neurotrasmitters involved in these systems could somehow just return to 'normal' balances after this increase in dopamine begins to resolve, addiction wouldn't be such a problem. But, it doesn't. Most drugs not only cause the release of certain neurotrasmitters (like dopamine), but will actually block the action of other neurotrasmitters that are important in managing the whole system. So, the result is a refractory deficit of 'normal' brain chemicals for some time after the drug wears off. There are dozens, hundreds, of chemicals involved in these processes, and while a particular drug may only influence a few key chemicals directly, many others are affected indirectly. I am simplifying this for understanding, but I don't believe to the point of inaccuracy.
There have been more than casual links identified between certain genes and addiction potential for alcoholism. In essence, some people have genes which cause certain areas of the brain to be influenced by alcohol far more than those without the gene. Normally, alcohol is not a highly addictive substance, and so prolonged use would be necessary for dependence to develop. In persons with this gene, changes occur in their brain after a few exposures to alcohol that would normally only be found in persons who have been exposed to prolonged use of alcohol.
Some drugs affect other key neurotransmitter systems affecting memory, concentration, and mood. Ravers are finding this out with alarming frequency, unfortunately, because the consequences of prolonged ecstacy type drugs can permanently damage the seritonin system. Seritonin is an important neurotransmitter that is linked with a host of disorders including anxiety, depression, chronic fatigue, obsessive-compulsive disorder, schizophrenia, idiopathic pain, hypertension, and migraine headaches. Numerous examples exist of college aged persons who have permantly damaged their natural seritonin 'balance' due to prolonged ecstacy use. I've heard one describe it as having a bad hang-over, for the rest of your life.
The bottom line is, there is no such beast as a "safe" recreational drug, nor is it likely there ever will be. Anyone who attempts to tell you otherwise is a bona fide idiot. There are risks, and those risks increase with the frequency or prolongness of use. Typically, the brain will restore its 'normal' balances within a few hours after the affects of cocaine, heroine, amphetamines, etc. wear-off, and excluding overdose or the rare reaction, there is no harm done. But, frequent, persistent or prolonged use can permanently alter or damage the brain.
This is no different than if I hit you with a stick. You will bruise, but it will go away. If I wait a few weeks before hitting you again, same thing will occur. But, if I continue to hit you with a stick in the same spot every few minutes, over and over again, I will eventually cause permanent damage.