The short answer is that they are supposed to be equivalent in medication delivered to your body.
However, the bioavailability of any generic drug to the original branded product can vary, and generics may vary between manufacturers as well. The FSA publishes a book called The Orange Book which lists the relative equality of generics.
However, variability in bioavailability can cause a problem in drugs that require exacting titration to reach a desired effect, such as Coumadin (Warfarin), Lanoxin (Digoxin) and Dilantin (Phenytoin).
In examples such as this, you can take the generic in place of the trade name product, but it would be best to stick with the same 'brand' of generic to avoid this issue.
There are numerous reports in medical literature demonstrating over and underdosing situations specific to this type of drug.
Also, and unfortunately, there have been a rash of generic manufacturers whose quality control leaves a lot to be desired. For example, Ethex was shut down by the FDA recently because of poor quality control. There were also a massive number of recalls for generic digoxin, with the tablets containing unreliable amounts of digoxin.
I take generics (I am a pharmacist) and I also monitor the effect to be sure that there is not an issue with the specific generic I am taking. However, if I ever need Digoxin, I will insist on Lanoxin (the original). The same is true for Warfarin -- I would insist on Coumadin.