I agree with the posts above, and would add:
Under current law, you can destroy, give away or have a firearm stolen without informing the federal and most state governments. They cannot assume that you have a firearm, even if you had a NICS check and filled out an FFL yellow form. The essential part of any registration scheme is that this is done away with and the person registered becomes tied to the arm for as long as the government is not properly informed.
After you register your arm, you are responible for it for ever more. If you claim you no longer have it, you become an instant felon.
Usually, you also give up your right to have a warrent of probable cause taken out to search you home and property as well. This is for the new "privelidge" of owning a fire arm. The police can search you or your property whenever they want to make sure you still have the firearm. Of course, they can arrest you for any other "illegal" thing or circumstance they discover during the course of this "honest" search for your arm.
Once they have pinned the weapon to you personally, there are many other tricks they can play, such as making you responsible if someone else commits a crime with the weapon (even if they do not know who that person is), imposing all kinds of "safety" restrictions upon you (usually costly and inconvenient), limiting your right to free speach if you talk about firearms "irresponsibly", imposing special "fees" upon you, etc. etc.
You see, the assault on the 2nd ammendment has cascading effects on all other civil liberties that you enjoy as well. We now need to stick to the principle of the Second Amendment as a personal right of all law abiding American citizens. Firearms registration is something that is unacceptable in America. It is now the cause celebre in determing whether or not the Bill of Rights, our basis of civil liberties for over 200 years, can be breached by an unprincipled president as a political expediant. If Clinton/Gore get away with it, more abuses will certainly follow.