So I guess the answer to the question is the same as almost every question in medicine... it depends.
For example, I would never touch Marshmallow Mateys but I love Lucky Charms and I am a big Coke fan but I hate the generic colas. Strangely enough I can't stand brand name Mac and Cheese but I love the Western Family Mac and Cheese.
So... it must be the same for things like drugs, right? Once again, the answer is, it depends.
For most medications generic is no different than the brand name drug. The brand and the generic are so similar in most cases that you are not even given a choice as to which you receive the pharmacy just gives you the generic. It has gotten to the point that many brand names have been nearly forgotten of certain drugs.
Now, for the exceptions to the rule. There are drugs that are referred to as narrow therapeutic index drugs. These drugs have huge differences in efficacy, side effects, and toxicity with very small changes in the amount of medication.
For the legal stuff, the FDA tightly regulates drug companies and their products. Most of the time when a new drug comes out it has gone through years of tests and reviews. When a generic comes out it also has to pass many reviews and tests to prove that it is within a 20% window of similarity to the brand name it is copying. So it can achieve drug levels in the blood between 10% above or 10% below the levels achieved by the brand name. For example, lets say you take Paxil 20 mg (a common medication used to treat depression, OCD, or anxiety) and then we draw your blood an hour later find you have 10 mg in your blood. Generic Paroxetine (the generic for Paxil) could have drug blood levels after one hour that could legally range from 9-11 mg. So there could potentially be a difference but it would be incredibly small, far too little for anyone to feel. Something we also have to remeber is that all generic companies are trying their hardest to get as close as possible to exactly the same, so often times they don't use the range the law allows them.
An interesting fact is that many generic companies are owned by the brand name companies so the brand and generic are made in the same factory bu just put into different packages, so they are the same.
An example of one of those narrow theraputic index drugs. Lets say you have epilepsy (you have seizures often enough to require treatment), and you are taking Depakote ER and you transfer your prescription to a new pharmacy and they fill it with generic Valproic Acid. There should be red flags shooting up everywhere! All drugs for epilepsy should never be switch without a doctors supervision. Even though the difference is incredibly small it is enough of a diffrence that many people have seizures despite taking their medication religiously after being switched to generic.
Now it goes both ways if you are well controlled on generic don't let the pharmacy switch you to Brand without talking to your doctor.
What it boils down to is if you are given generic medication right of the bat, don't worry, it is just as effective as brand. If you are on brand and are switched to generic chances are there won't be a difference but don't be shy about asking. Ask the pharmacist if you will be okay, it is his/her job to know, make them earn their money. Also remember that for everything other than drugs brand versus generic does matter, at least to me.
