OK, I figured I should start a kitchen essentials post to get a solid list together on kitchen minimums. I figure you can find many similar lists online & in cookbooks, but hey, I'll throw my chef's knife into the ring too! This is really a list for people who aspire to start cooking more seriously.
1. Good quality chef's knife or santoku knife. Anywhere between 7" - 10" blade should be sufficient. Spend some money on this, $50-100. With some care it will last you a lifetime, and will not let you down. Spend a few dollars more and get a sharpening steel to keep things cutting sharp. With some care you can do almost anything with this knife.
3. Cutting Board. I found some great, large cutting boards at IKEA for a fraction of what you would pay at a "gourmet" store or a hardware store. Something 36" long x 24" wide would be good. Get a smaller cutting board (9" x 12") too, handy for side projects.
3. A 12" cast iron skillet. Will work as a saute pan or for stir frys. Holds heat incredibly well, and will last your entire lifetime with good care.
4. Pots and pans. I recommend stainless steel, it'll last longer than Teflon although not as easy to clean. Get one big pot for boiling pasta & making soups/stocks, and 2-3 small saucepans for sauces, vegetables, etc.
5. Pepper mill. Fresh ground pepper tasted so much better. Buy a sturdy wood one, looks classy and will last a long time.
6. Utensils: a nice inclusive kit is the OXO Softworks kit. Comfortable to use & handle, built to last. You'll need at least 2 spatulas, 2 big spoons, a grater, a whisk, a vegetable peeler, a can opener, and a bottle opener.
7. Canning Jars. Ball Wide-Mouth canning jars are a cheap and cost effective solution to storing spices, oils and other ingredients in an airtight environment. I like the pint jars for spices & vinegars, the quart jars for oils & dry goods. Jamie Oliver (the Naked Chef) nails the jar lids and screwtops to the bottom of the cupboards in his kitchen, and screws the spice-laden jars into the lids when he's done using them...see, handy!
8. Digital Instant Read Thermometer. Polder makes one that goes up to over 400 degrees F, making the thermometer usable even for checking the temperature of oil for deep frying. Important for checking the temperature of meats to ensure doneness, especially chickens, turkeys and roasts.
Of course, this list hasn't talked at all about baking or other specialty tools you might need. So I guess that's enough for now.