Gadgets

I am not a huge fan of fancy kitchen gadgetry.  I my kitchen is small, and I was a starving student until a year ago.  I put together my first kitchen from thrift stores, for under $50.  And even if I had all the space and money in the world, I still wouldn't think I needed an avocado slicer.  (I already have one.  It's called a "knife.")

That said, there are a few things I think every kitchen needs, and several that aren't really necessary but that I love and would hate to live without.  Here they are:

Basic Kitchen Tools

 Knives
 You need at least one big chopping knife, one paring knife, one large, serrated bread knife, and one small or medium serrated knife for tomatoes.  I have a Wusthof santoku that I use more than all my other knives combined and that I absolutely love.

Pots and Pans
You need, at minimum, two small/medium saucepans, a pot large enough for pasta and soup, at least one large frying pan.  Lids are essential.  I recommend against non-stick, as it wears out quickly and, when it does, it releases icky toxins into your food.  I prefer cast iron, which is non-stick if you treat it right. 

I have a couple of thrift store stainless steel saucepans, a pasta pot, a huge stock pot that I got for brewing beer, three cast iron pans, and two enameled pots.  I use the enameled pots as fry pans when I'm making something acidic that might damage the seasoning on the cast iron.

Mixing Bowls
I recommend glass, as it can be microwaved and, covered in tinfoil, be used as a baking dish.

Bakeware
At a minimum, you need a 9 x 13 inch pan, a cookie sheet, and a casserole with a lid.  If you do any significant amount of baking, you'll also need a loaf pan, a pie plate, 8 or 9 inch rounds,  and an 8 or 9 inch square pan.  Other than that, it really depends on what you like to make.

Cutting Board
Preferably two (one for garlic and onions, and one for stuff that you don't want to taste like garlic or onions). 

Measuring Cups/Spoons
You don't even need separate liquid and dry measuring cups.

Spoons/Spatulas
I use my silicone, wooden handled spatula for just about everything, because it doesn't hold flavors and won't melt if I just leave it in the pan.  You also need a couple of wooden spoons (one for spicy foods, one for sweet foods), a slotted spoon, tongs, a ladle, a whisk,  and a wide, flat spatula for turning (mine is metal, and I love it).

Grater/Zester
You need a Microplane zester for parmesan, nutmeg, and citrus zest, and a coarse grater for everything else.

Colander/Strainer
I have a large mesh strainer that I use for everything, but a colander is probably easier to clean if you make a lot of pasta.

Handy, but Non-Essential, Kitchen Tools

Hand-held Juicer
This becomes a necessity if you make as many margaritas as I do.

Mini Food Processer
I keep mine on the counter and use it for finely chopping pain-in-the-butt stuff like nuts and copious amounts of garlic, and for pesto, small batches of hummus, and emulsifying salad dressing.  I love that with it, I can get by without a larger, much more expensive food processor.

Blender 
Great for making over-ripe fruit into smoothies in the summertime, but that's about all I use it for. 

Toaster Oven/Microwave
These make re-heating easy, plus it's nice in the summer to be able to bake something small without overheating my un-air-conditioned apartment.  But completely unnecessary.

Silpat
This is a great substitute for parchment paper (it is completely non-stick). 

Thermometer
This takes the guesswork out of figuring out when your bread, and meat, are done.  But I got by without it for years, because I didn't do slow roasts of meat and didn't bake bread. 

Mixer
You can (and I do) survive without a fancy KitchenAid stand-alone mixer.  You can even get by with just a whisk, but its a huge pain to make meringue or whipped cream without a motor.

Crock Pot
Completely unnecessary on the weekends when you can hang around the house and monitor stuff on the stove or slowly roasting in the oven.  But it's so nice to throw a few ingredients together in the morning and come home to an aroma-filled house at night, and they're easy to pick up at thrift stores.

Enameled Pots
It's really, really nice to be able to go from stove-top to oven to table, especially if you're washing the dishes by hand.