This is what I feel every kitchen needs to be complete:
Quality Stand Mixer
A good quality strong mixer is essential from a meringue, through to a pasta dough. An inferior mixer will burn out and fail very quickly, when it comes to breads and baking the quality of your mixer will most definately determine the final outcome of your meal. Personally, I use a Kitchenaid 5KPM50 which is a semi professional model with a thermo cutoff switch to protect the motor (essential with pasta doughs).
Digital Gram Scale
As you get more proficient in baking, you quickly stop using cups and spoons to measure things and instead rely on the scale solely, including measuring water. A scale that is accurate to the gram is critical, and a small jewellers scale accurate to a tenth of a gram is ideal when you begin working with spices. From "scaling" the dough (measuring the pieces) to assembling ingredients, the scale will become and essential piece.
Digital Thermometer (probe style)
When you cook meats, it is often easier to cook it until the center is at the desired temperature instead of timing it. There is nothing worse than putting your meat on for a specified period of time and finding that it is undercooked or overcooked due to a slight miscalculation in the weight of the meat cut. A thermometer solves this, you begin checking the meat before its due time, and so on until it is just right. It is also essential in candy and other forms of sweets preparation.
Infra Red Thermometer
When you begin working with chocolate and candies, you often need rapid temperature control, especially when tempering chocolate where being out by a degree can ruin all your hard work. While these are quite expensive, they are essential for success as they are rapid and accurate. Not useful for measuring into a mixture or meats however.
Electric/Gas/Induction ... the debate will forever rage on. In a working kitchen, electric and induction are not practical which is why gas will always reign supreme on a commercial scale, however in a home kitchen induction should be your first choice. From a "green" perspective its the most energy efficient method of cooking (least energy wasted in heat) and it is also the fastest to bring dishes up to temperature. Expensive models have accurate temperature control for simmering and other cooking styles, but for the most part a cheap portable induction hob is all you need. The only warning, don't buy one if anyone living in the house (or could be a guest) has a pacemaker, as the magnets used by induction *could* interfere (keep them out of the kitchen while its on).
This is also a personal thing. Gas or Electric? Well, Gas provides a "wet" heat as the gas combustion also produces water vapour, which can be good for baking breads and meats, however you may not want a wet heat, so an electric oven is the choice. At least with an electric oven you can add water dishes to moisten the air, while you can't easily dry the air in a gas oven. If you have the space, a Pizza oven is the ideal, but they can be expensive to build.
Good quality knives with sharpener
You will cut yourself more with a blunt knife, than a sharp one. Learning knife skills is absolutely critical to preparing dishes, and a good quality knife set will make this chore much faster and safer. I personally use Shun knives from Japan, however they are expensive and lose their blade easily. Also chose a plastic or wooden chopping board, not glass, marble or any hard surface or you will dull the blade. And another thing ... NEVER wash your knives in the dishwasher, always wash by hand in the hottest water you can hold your hands in, and dry immediately after washing before storing on either a magnet or in a case. Timber chopping blocks can accumulate cockroaches ants and the likes as well as moisture.
Quality Cooking Set (Saucepans, etc)
Cheap saucepans will need to be purchased over and over again, while a good quality heavy riveted saucepan set (all steel) will last you a lifetime. Where possible get them plain without any non stick garbage, and make sure the handles are riveted with no silicone or anything so they can go straight into the oven. If you have an induction cooktop, make sure a magnet sticks to them or else they won't work on the stove.
Piping Bag with assortment of fittings
Unless you do a lot of pastry, cakes the the likes you could well overlook this, but there comes a time you want to make something special and you just can't do it because you need a piping bag. These are cheap and last forever, and if you get one now, you will have it when you need it.
Plastic Scraper & Rolling Pin
Along with the rolling pin a plastic scraper is a godsend when working with doughs. They become an extension of your hand allowing you to work with the dough without getting it everywhere. The scraper makes scaling dough a very simple task, and the rolling pin is essential come any time you need a thin flat dough (Pizza, Croissants, Puff Pastry, etc).
Measuring Cups and Spoons
While not heavily used in the bread world, when it comes to pastries they become more prevalent. They are also essential for the myriad of recipes out there that have relied on this form of measuring ingredients.
If I have missed anything, please feel free to add your suggestions.