A damned good set of pots and pans- at least 2 frying pans (I have 3); 1-qt, 2qt and maybe a bigger sauce pans (having 2 “medium” sizes is always helpful0; a good stock pot (I have 2). Don’t forget baking sheets.
Utensils- a few wooden spoons/spatulas just in case, but I try to stick to metal (less potential contamination)- a big solid spoon, a big slotted spoon, two spatulas, a pasta thing (spoony-thing with teeth), a pair of tongs, and a couple of those silicon spatulas for getting cake batter out of the bowl. Also a 1-cup and a 2-cup liquid measuring cup, a set of dry measuring cups, and a set of measuring spoons.
Some specialty pots & pans- a good quality wok, an electric frying pan (I have my grandma’s and it still rocks).
Mixers & blenders- a hand blender (that stick thing), a standard blender, a hand mixer and a stand mixer. Each of these serves a specific purpose and if you need one, it can be difficult to substitute another.
Pyrex- at least 3 or 4 Pyrex glass bakers with lids (I have my mom’s).
Knives- I am a firm believer in great knives. A good basic cook’s set should run you well over $100, but don’t scrimp- nothing sucks worse than a shitty knife. Also get a specialty set for paring and a good set of steak knives.
Cutting boards- I rarely use wooden cutting boards anymore (contamination issues). Rather, I have a set of flexible plastic cutting boards that I use for prep (and everything else- one lives on my counter). Some are color-coded for specific foods (meat, fish, veggies) but I don’t bother with that- I just wash & bleach them in between jobs. A spray bottle of bleach solution near the sink is handy for all sorts of things.
Appliances- a toaster, a coffee maker, at least one tea pot, a juicer.
Fun stuff- extras like loaf pans, food mills, milk shake machines, indoor grills- handy but not necessary (except the grill- if I didn’t have a BBQ, I couldn’t live without it).
I’m sure I’m forgetting a bunch of stuff, but the Dopers will catch me up! 