Whelping Items Checklist
Note: This checklist is to be used as a guide and does not in anyway replace instructions that should come from your veterinarian.
A good veterinarian A vet that you know is going to be at the other end of the phone when you need them at 4 AM (you gave them a heads up, of course).  One that will provide the recommended oxytocin, calcium and/or dopram in advance, to use under their supervision while on that phone for emergency situations.  Obviously, you must already have a good relationship with this vet.  Be sure and have the emergency phone number handy.
Whelping box or puppy pen Of a suitable size to suit your bitch and number of pups, line with newspaper for whelping.  You will need lots of newspaper (keep changing as needed during whelping).  The bitch should spend at least a few days in the pen (assuming crate trained) prior to the whelping due date.  A folded up bedsheet or mattress pad is good to line the pen after the puppies are born.  This will need to be changed a few times a day.
Heat lamp with a 100 watt white bulb 
(heating lamp bulbs can burn pups)
When whelping is finished, to hang a couple feet above the whelping box or pen for the first week to keep the pups at 75 - 80 degrees.  A thermometer to place in the pen is necessary to test the temperature.

To take note of the time of events.
 One or two clean or new cardboard boxes  The tops of copier paper boxes are great (for small breeds), with a heating pad in the bottom (on low) covered with a towel.  Use a second towel or faux sheepskin to cover the pups.  This is used anytime you need to separate the pup(s) from the mom (during whelping the next one, etc.)
Lots of towels You need some for cleaning up after drippy messes, some to go in the cardboard box, and some of a smaller size to wipe and dry puppies with.  I have some old terrycloth diapers that are perfect to dry puppies!  Otherwise, cut some old towels into 12 x 12 inch squares.  Plan on three per puppy.  These are also good for holding puppies should you need to revive them, or swing them down hard to clear their lungs.  Hold it tight in a towel or it will go flying.  I also use the small towel for gripping if I need to help a puppy be born (for example a breach birth).
Paper towels Cleaning up messes
Garbage bag Place to put paper towels and occasional placentas that a bitch may not get to clean up.
Coop Cup (or other water vehicle) A coop cup placed on the inside of the pen (where the bitch can reach it, but not in the way) is good so the hot and panting bitch can get some water to help stay cool.
Baby scale, Food scale or Postal scale I like to use a postal scale that weighs in ounces.  I put a sturdy plastic storage container on top and calibrate it to zero.  Pups should be weighed at birth, after they are cleaned up.  You will use the scale to weigh the pups every day for a week or more (to be sure they are thriving, and decide whether to supplement with formula), then once a week to track their growth progress.
Electric heating pad To put in the bottom of a box for interim storage of puppies, and later, to use in the whelping box or puppy pen to keep a warm spot for puppies.  Some breeders don't use these in the pen because some bitches will chew the cord.
Hot water bottle(s) An alternative for keeping a warm spot for puppies in the box or pen.  These are necessary for trips to the vet.  Put them in a box covered by a towel.  Latex rubber gloves filled with water and tied work great too, and can be re-warmed in the microwave. 
Latex gloves They aren't necessary, though will help keep your hands from becoming stained if you end up handling placenta in an emergency situation.
Notebook and pencil You want to write down the times that you observe behavior changes in the bitch, when pushing starts (for each pup) and when delivery occurs.  You want to mark off that each placenta is delivered.  If you mark pups for identification, make note.
Sterile scissors (3-5 minutes in boiling water) Some breeders like to tie cords with the unwaxed dental floss then cut them with sterile scissors and dab them with iodine.  My vet prefers that I tear them with my fingers.  Check with your vet.
Un-waxed dental floss See 'sterile scissors'
Iodine (for tummy cords) See 'sterile scissors'
Colored yarn or Nail Polish (several different colors) Some breeders use a different colored yarn tied around the neck of each pup to tell them apart.  I like to use Nail Polish (on a dry pup) on a back or foot to mark mine. This may occasionally need to be re-applied, though I prefer that to the risk of getting tangled in the yarn.
Baby suction bulb Some breeders like to have one of these on hand.  They will clear the mouth of fluid, but not the lungs.  I usually employ the 'swing the pup down hard' technique to clear fluid.  Ask your vet for instructions.  Don't swing the pup near anything that you care about getting stains on!  In the bathroom is usually safe if you have linoleum floors.
Rectal thermometer The thermometer is used to take the bitch's temperature twice a day for the week before she is due to whelp.  The bitch's temperature will drop a degree about 12 hours before she is due to whelp.  It is necessary to take the bitch's temperature after whelping once a day to watch for signs of infection.
Crate in the car It is not a bad idea to have a crate in the car (or nearby the car) so in an emergency situation, you can make a quick get away to the vet's office.  If you have a large breed, a friend assisting might be a good idea.  Think about how will you transport existing puppies as well.
Baby Bottles / Nipples / Formula You may need to supplement a puppy if it is not doing well, or if the bitch rejects it.  Have these on hand just in case.  The bottles can also be used for sugar water or Pedialite as recommended by your vet.  I find that it is easier to use a 3CC syringe to feed a puppy.
Feeding tube/syringe A feeding tube is good for feeding weak puppies.  Ask your vet for details.

Other tips

One breeder gives the whelping dam vanilla ice cream as a pick-me-up. She loves it and will always take some.

Keep books on whelping close at hand.

Keep a collar on the bitch and a leash handy so you can walk her outside in between pups. They love to whelp under porches.

If you have a tip to add to the list, email me.