Electrolysis:

I prefer to remove rust using electrolysis.  This is a simple procedure that is particularly well suited to large parts and will not damage the original parts in the way that chemical or manual removal will.  The method is simple: submerge the rusted part and an electrode into a "magic" solution, then pass a current between the two using the solution as a conductor.  The solution is made of 1 tablespoon of washing soda (not baking soda) per gallon of water.  Add the soda to the water, and use warm water to help dissolve the soda (it doesn't matter if the water gets cold later). The electrode can be made of any ferrous metal (iron) or stainless steel.  I have used a railroad spike and an old steel dust pan; if it rusts, it's probably fair game.  Don't use galvanized metal or aluminum.  You want the electrode to as large or larger than the part you're working on (the bigger, the better); you can't use a nail to clean a bumper.  Although the process will not harm the original part, it will destroy the electrode (unless the electrode is made of certain alloys of stainless steel), so don't use the wife's good pans.

To de-rust a part, place the part in a non-metallic container (garbage can, glass baking pan, plastic bucket, etc.).  If you have an odd-shaped part, make your own container.  I've used garbage bags inside cardboard frames.  Place the electrode close to (but not touching) the part.  You can put a sponge in between them to keep them apart.  Any area that is to be cleaned must be submerged, and it works more efficiently on the side of the part closest to the electrode.  If possible, form the electrode to go completely around the part.

Attach the negative lead from a battery charger to the part, and attach the positive lead to your electrode.  NOTE: Polarity is crucial.  You MUST attach the negative lead to the part.  If you get the polarity wrong, you WILL destroy the part.  As I mentioned earlier, this procedure does destroy the electrode.  It will also destroy the clamp on your battery charger if the clamp is submerged.  I suggest attaching a length of heavy gauge wire to the electrode, then attaching the lead from the charger to the other end of the wire outside of the solution.  Turn on the battery charger, and watch the action.  You should see small bubbles coming from your part, and you should see a small current draw (2-4 amps) on the ammeter of the battery charger.  If you have an automatic battery charger, you may need to set it to the "start" position, as the small current draw will fool the charger into thinking its attached to a fully charged battery, so it will shut down.  If you don't see anything happening, make sure you have good connections, make sure the parts are close, and make sure your charger is putting out current.  You can also stick your hand into the solution (it's harmless).  You will feel a slight tingle from the current.

After the process has been working for a while, you will notice that the solution is quite disgusting.  It doesn't matter; it will keep working.  Let it go for a couple of hours.  You can't damage your part doing this, so you can't leave it too long.  When you pull the part out, the formerly rusted areas will be black.  You can remove this by rubbing lightly with your fingers, a plastic pot scrubber, or your wife's toothbrush. If the black doesn't come off, put it back in the solution for a little while longer. You shouldn't have to use steel wool or a scouring pad.

When you're done, you can just dump the solution out.  It's harmless and non-toxic.

Vinegar:

If you have smaller parts, you can derust them using plain vinegar.  Submerge the parts in the vinegar, then heat the vinegar on a stove or hot plate.  This will stink.  If you do not live alone, do it outside or when no one else is home.  NOTE: Vinegar is acetic acid.  After removing the rust, it will continue to slowly eat away at the part.  It will also leave the part with a "pickled" or weathered look.  As such, you must be careful if you're using vinegar (or any acid) to remove rust from parts that aren't destined to be painted.  You should also note that the vinegar will have the same effect on any container used to hold it.  Either use an old pot, can, etc., or use glass.

Final cleanup:

After the rust is removed, you must be careful that the parts don't immediately rust again.  I have found that a quick dip (or wipe) in rubbing alcohol or paint thinner helps to displace any residual water.  Follow this with a couple of minutes in the oven or a once-over with a hair dryer and you should be fine.