Before I write a big essay on what you need in a well-equipt kitchen, I’ll point to some other opinions.
Anchulis posts her 3 most underrated kitchen tools – chopsticks, a citrus reamer, and her toilet. I completely agree with her. Shylo, in the comments to the Anchulis post, mentions counterspace – the third most important part of a kitchen after the sink and heat producing unit.
Butterpig lists a top ten equipment list, with which I’m in complete agreement. Basically that’s the essay I would have written, except I would make the addition of a cleaver or santuko type knife, and a non-stick pan. The knives are a preference, and you could probably do fine with just a chef’s knife, but for perfect omlettes and fragile fish fillets, you just can’t get by without a good quality nonstick.