Backpack
This is what carries all the other stuff.  It's important to have a good backpack.  I use a Jansport Yosemite external frame I bought from a friend for $75 ($200 new) and I carry about 50 lbs.  Carla uses a Kelty internal frame we bought at Costco for $50 and she carries about 30 lbs. External frames focus the weight more on the hips and less on the back and therefore can carry more weight with less effort but they are top heavy and not as stable going up and down hills. 1998 Update:  We are now contemplating going strictly external frame -- you can carry more weight with less pain, they're better for the kids, easier to pack, etc.

Sleeping Bag
A good bag is absolutely essential.  It needs to be warm (even when wet) and light.  We have some Caribou bags (-20 degees) I bought 13 years ago for $100 each.  They're a little heavier than modern bags but are still in great shape, are very warm, and zip together for extra comfort.  1998 Update:   Just bought some new bags (+15 degrees) because they are much lighter & still warm enough for most of our trips.

Sleeping Pad
Sleeping on the ground is for youngsters.  There's nothing like sleeping on a cold rock all night to make your back hurt for a week.  Pads come in many styles & prices.  We've got a couple of used Thermarests ($50 new) & we bought some closed-cell foam pads for the kids. 1998 Update: Bought some brand new, full-length, non-slip Thermarests (app. $60 each) for Christmas presents to ourselves -- what luxury!!

Tent
A place to go to get away from the wind, rain, & bugs.  Home away from home.  We have a nice 2-person , 3-season REI Half-Dome I got on sale for $100.  Not so great in the pounding rain but very light & easy to set up.  Bought a great 3-person, 4-season Sierra Designs tent on clearance for $200 (regularly $350) that we're going to use when the kids go with us or the weather is nasty.

Tarp or Tent Footprint
A lightweight plastic or waterproof nylon tarp protects the tent bottom from rocks, sticks & moisture. Doubles as a lean-to, wind or sun block, etc.  ($5-25)

Stove (w/fuel)
Essential for cooking meals & boiling water.  We have a Gaz which operates on a butane/propane canister. The stove is tiny & folds up very small.  The canister is a little heavy but very convenient to use (adjustable flame) & does double duty by fueling a small lantern.

Water Bottle
We carry 1) a Nalgene wide-mouth w/insulated holster ($15) which is great for reconstituting dried food, packing ice cubes, etc., 2) a 1 liter Platypus ($6) which is light & rolls up small, and 3) a Jansport bicycle bottle with spout.  The kids carry old Gatorade bottles.  1999 Update: Bought a Platypus with a "Duckbill" tube ($14).  The bottle fits in a pack pocket & the tube hooks to the shoulder strap for hands-free drinking along the trail.

Water Filter
Water is heavy so we carry a quart each on the trail.  Once we get to where we're going we fill up all the bottles & the platypus.  There's lots of expensive water filters but we've found our cheap Timberline ($25) works just fine.

Purification tablets - VERY IMPORTANT
In case the filter breaks down.  Beware of Giardia -- always filter, purify or boil any water in the wild.

Matches
Regular, strike-anywhere for normal use.  Waterproof for rainy days.  A small butane lighter is handy.

Rope
Lightweight nylon cord to stake tents & tarps, hang food in a bear bag, clothesline, etc. ($3)

Pocketknife
Swiss Army knife with sharp blades, awl, corkscrew, bottle & can openers, screwdrivers, toothpick & tweezers.  Most useful tool there is.  ($10)

Maglite
Small, powerful flashlight with handy holster.  ($10)  Don't forget extra batteries. 1998 Update: Got one of those headband things that hold the flashlight hands-free.  Great for cooking, reading, etc. after dark. ($4)

Survival Kit
Aluminum or plastic waterproof container small enough to fit in a pocket containing a number of helpful items to get through tough times.

1st Aid Kit
Zippered pouch containing numerous helpful items in case of emergency, injury or illness.

Personal Care Kit
Zippered pouch containing numerous helpful items to keep yourself clean and comfortable.

Clothes
Just enough to stay warm or cool and protect yourself from the elements.

Cooking Gear
Just enough to cook a warm meal after a long day of physical exertion.

Miscellaneous
Reading book, glasses, camera/film, Thermorest chair, camp towel, wash cloth, binoculars, cards, map, lantern, walking stick, etc.