My recommendations,:

-kitchen scale, the digital OXO with the pull-out display is great
-candy thermometer
-instant read meat thermometer
-hand mixer
-blender
-microplane
-box grater
-2 good chef's knives, at the very least. we love our Meissermeister set.
-wooden citrus reemer, for juicing any citrus
- 1-2 sets of dry measuring cups, since the US is still using volume measurement for baking and most recipes here are written that way.
-wooden cutting boards, Boos makes great ones
-castiron dutch oven, for braising, deep-frying, and No Knead Bread
-OXO tongs
-wok
-Pyrex liquid measuring cups

The "Not essential, but rather nice to have" list:

-Kitchen Aid standing mixer with assorted attachments
-food processor, 10 cup or more
-Thermapen
-ice cream or gelato machine
-All Clad pans
-Weber Q grill
-Cameron stovetop smoker

A decent Chefs knife and a good non stick pan.

My "use all the time" items are:
-chef's knife (Ya beat me too it Jon Walker)
-plastic cutting board
-non-stick pan (as mentioned by Jon Walker)
-large sauce pan (to cook a pound of pasta)
-"regular" size sauce pan (to cook the pasta sauce or hard boil eggs, or cook a single-serving of pasta, or cook oatmeal, yada yada yada)
-silicon spatulas
-prep bowls
-kitchen scale

here are my must haves (in addition to some items mentioned above)
*well-seasoned cast iron pan
*immersion blender
*oven thermometer (temps can be off on older ovens)
*knife sharpener
*wooden spoons

http://www.nytimes.com/2007/05/09/dining/09mini.html?pagewanted=all
I trust Mark Bittman for anything kitchen and it's his take on the above.

My kitchen ended up being ...

Cooking
Pasta pot
10in non-stick fying pan
Sauce pan
8in wok
Cutting board
Salad spinner (doubles as colander)
9in chef's knife (+small sharpening stone)
bread knife
kitchen scale
Immersion blender (i'm lucky mine has a mixer attachment)
Pasta machine!
Splatter guard (for frying/draining stuff)
Thermometer
Microplane
Mandolin set.

Baking
9" round
8" square
Muffin pan - 6
1 big mixing bowl
Consumables
Parchment Paper
Press N Seal (instead of cling film, much more useful for sous vide-ing)
Foil
Ziplock Bags
Stainless steel measuring cups and tbsp/tsps

Most of what is above plus:
-a fine mesh strainer
-colander
-a ladle

I could survive without my microplane and my stand mixer, but I'd never want to!

Moving to my new home, I only had a wok, a small pan, one prep bowl and a knife. I survived a month. since then have been collecting more kitchen "junk". lol

I couldn't live without my Kitchen Aid Mixmaster, Chef's knife & Microplane. Check out this list of basics as well. Definitely buy the best you can afford and remember you don't need the whole knife kit unless you're a chef. http://foodfromourlife.wordpress.com/equipment/ think about what you use all the time now, good garlic crusher, morter & pestle, good potato peeler, wooden spoons, whisk, egg lifter, ricer (to make gnocchi) you are going to have a wonderful time buy all new things! Have a safe trip!

Mind you, I'd be taking my chef's knife steel etc with me in luggage stowed in the hold.. no way would I leave those behind.

In addition to the above:

Cotton kitchen towels
Wooden spoons
Garlic press
Lemon squeezer

Utility knife
Immersion blender
Can opener (definitely a vintage Swing-A-Way, like the one shown in the photo above)
Sunbeam Oskar vintage food processor, powerful, yet compact
Foley food mill (vintage ones are the best)
Cast iron skillet
Stainless Dutch oven with a heavy bottom
Wood spoon--the older, the better
Spatula (my favorite is a vintage Flint stainless slotted spatula)
Ladle (I like the vintage Flint stainless ladle)

Personally, I'd skip the regular stores and go straight to an estate sale where you'll get the quality old stuff, and spend far less, too.