Stand Mixers make things a lot easier- I <3 our Kitchenaide
Bread Machine, if you're into bread.
Slow Cooker
Pots of various sizes (4-6 cup, half gallon, 1-5 gallon/stock pot)
Frying pans- we need 3 for Mexican night.
Measuring equipment
Blender
Coffee Grinder and French Press
A loaf Pan or two
Baking sheets
Pizza pan (or pizza stone, if you prefer)
Durable spatulas- rubber AND metal.
Wooden Spoons
Stone/Porcelain bakeware
Glass bakeware
Metal bakeware
Good knives- At least one each of serrated, non-serrated, and bread. Possibly more than one if you plan to cook multiple dishes at once.
Pot holders and/or trivets, unless you have stone counters
Well-stocked cupboards
Also, while a rice cooker is not "essential" it's certainly handy. If you're just moving into the realm of cooking from scratch, and not sure which small appliances to get first, I'd recommend starting with the slow cooker and the blender. It's very nice to know you can put some ingredients in a pot in the morning (or the night before), press a button and, barring power failure, come home to a fully cooked meal. One of the most frequently cited reasons for going out instead of cooking is a lack of time. If you're confronted with dinner when you get home, that excuse goes right out the window. Then when you're full, you can wash the pot, prepare it for the next day, and press the button on your way to work the next morning- cheapest ones at Wal Mart ar like $20 on sale, and you can probably find one for even less on CL, or free on freecycle. A bread machine will offer you the same luxury for fresh bread.
Oh, if you live in a climate that has non-rainy summer days (ie, NOT Oregon :{D ), I highly recommend a grill of some kind, but I can't bring myself to deem it essential.