Measuring Cups and Spoons- These come in either metal or plastic, and they’re incredibly important when it comes to cooking and baking.  It might also help to have a large, glass measuring cup for liquids.  

Spoons- Every cook should have at least one wooden spoon, one slotted spoon, and one ladle.  These will cover all the basics: mixing dry ingredients, mixing wet ingredients, stirring foods as they cook, and serving soups or stews.  

Knives- You should have at least one long, sharp knife and one small, sharp knife for chopping, dicing, paring, and basic cutting.  

Spatula- You’ll need two different spatulas.  One should be a rubber-ended scraping spatula for baking, and the other should be a flat metal or plastic spatula for flipping pancakes, omelets or burgers.

Whisk- If you plan on cooking or baking with eggs, a whisk is important to have.  Whisks incorporate air into the mixture, unlike a regular spoon.

Vegetable peeler- When it comes to getting that pesky skin off your carrots and potatoes, it’s much safer to use a vegetable peeler than to try your luck with a knife.   

Corkscrew and bottle opener- Not every bottle of wine has a screw-top, so make sure you have a corkscrew.  Buy one with an attached bottle opener and you’ll save yourself a few bucks. 

Can opener- Many cans nowadays have pop tops, but not all of them.  There’s nothing worse than realizing that soup you were planning to have is no longer on the menu. 

Grater- It’s true you can buy pre-shredded cheese, but sometimes recipes call for you to shred vegetables, chocolate, or other ingredients.  It’s best to have one on hand.  

Mixer- Unless you have biceps of steel or hours at your disposal, you’ll want at least a small hand mixer.  Or you could choose to invest in a large stand mixer, instead.  A stand mixer will cost significantly more, but a high quality one will last for years.

Colander- You’ll need to strain things like pasta and vegetables, and having a colander on hand will make things much easier.

Frying pan- This will come in handy when you’re making stir-fried dishes, meat dishes, omelets, and many other meals.  

Pots- One large pot and one medium-to-small pot are absolutely necessary in any kitchen. 

Cutting board- Unless you want to destroy your counter tops, a cutting board is a must.  Plastic cutting boards are often easier to clean than wooden ones.

Mixing bowls- You’ll need at least one large mixing bowl.  The bowl can also be used for serving salads or other dishes.

Are you a novice cook?  Here are some other articles that may help you out:
Dictionary of Herbs and Spices
Cooking Terms Glossary
Food Storage Guidelines