Mixers - Most of us have a hand mixer. It works well for many recipes. Be certain to spend a little more for one with various speeds. It makes a difference when whipping cream or beating cake batters. I also have a heavy duty standup mixer. I consider that critical for many of the recipes I make, including angel food cakes and large amounts of cream or batter. A good standup mixer will also knead dough and some have attachments for making pasta shapes, grinding meats and even slicing. It is well worth the price and the space it takes on the countertop. It is a good idea to purchase an extra bowl for recipes that take two different preparations, such as whipping cream and egg whites. That way you don't have stop to wash and dry the bowl before proceeding.
Processors - Doesn't everyone have one? Maybe not. I have two different sizes. There is the large processor and my old standby, the mini-processor. Both are necessities in my kitchen. When choosing a large processor, you must consider what size you need and if you want extra disks. The mini-processor is ideal for small quantities, since they never chop as well in the large processor. I use mine more often than the large one, which I use mainly for making nut butters. Now they make processors that come with small and large bowls.
Coffee and Spice Grinders - I must admit that I don't grind my own coffee. However, the coffee connoisseur will probably want a coffee grinder and, if he or she also grinds spices, will need two. I have an electric spice grinder and I absolutely love it. I use it for all sorts of spices and seeds, and it even grinds small amounts of bread for crumbs. The bowl of a spice grinder should be removable for easy cleaning and made of stainless steel to prevent odors from being absorbed into the surface.
Toaster or Toaster Oven - Sometimes I miss my old toaster, a hand-me-down from my mother. However, I don't have room on my countertop for a toaster and toaster oven. I must have the oven. It toasts four slices of bread at one time. It is great for baking three or four potatoes rather than heating the big oven. It also heats small amounts of hors d'ouevres. Leftover pizza stays crisper than when reheated in the microwave. Mine also has a 'top brown' feature that makes great cheese toast without frying in the pan. It also has a broiler function which is handy for one or two portions of meat. Now they come with additional bells and whistles that I just don't need.
Countertop or Immersion Blender - I have a countertop blender, but don't use it very often. It is stored in the laundry room. I do, however, use my hand immersion blender often. It is superb for blending sauces or soups without making another bulky appliance dirty. Foods are blended directly in the cooking pot, not in batches. And it takes up much less storage space.
Electric Grill/Griddle - There are many nice stovetop grill and/or griddle pans that are great if you have a gas range. However, those of us who have ceramic stovetops cannot use them. I tried one that is specifically for ceramic tops and it just does not do the job. So I finally purchased an electric combination griddler that has interchangeable grills and griddles. It can be opened to lay flat or closed to do foods like panini. It works very well and cleans very easily.
Waffle Maker - There really is not much to say about a waffle maker except that you will need one if you want to make waffles. Mine is fairly basic and inexpensive. It is round with deep grooves, various temperature and texture settings, an on-off light, and it beeps when the waffles are done. There are many different types, sizes and brands available so do your research to make certain you get what you want.
Slow Cooker - Slow cookers are useful for busy people who need to start a long cooking dish in the morning so they can do other things during the day. They also come in handy when you need extra cooking space for a large gathering, or for transporting foods to a potluck. There are many different sizes, so plan wisely and consider your needs before making a purchase.
Dehydrator - This is not for everyone but, if you have a vegetable or herb garden, it is very convenient. It dries foods so much more efficiently than the oven, microwave or sun (unless you live in a very low humidity, sunny region). My dehydrator is stored in a closet, but is easily accessible when the herbs are in season. The size and power you need depends on the amount you will be drying at one time.
Bread Machine - If you like to make bread, you might want a bread machine. It really makes bread making easier when time is an issue. You can use it to make the dough, then bake the bread in the regular oven. I prefer homemade breads to store-bought because I can control the ingredients. Most of the machines have timers so you can place the ingredients in the bowl and set the time for when you want it done. I love making bread in my standup mixer, but this is less mess and so convenient. You don't need the most expensive. Shop wisely. An important consideration is counter space. If you want to use it often, find a place for it. I keep mine in the laundry room and it is easy to move to the kitchen.
Ice Cream Maker - If you love ice cream or frozen yogurt, give this some thought. As with everything homemade, you can control the ingredients and make frozen desserts without the preservatives. You can also make sherbets. Ice cream makers are great and lots of fun. If you have kids, consider the crank-style so they can get in on the act. Otherwise, go for an electric.
Knife Sharpener - This is mentioned on the cutlery page but is worth mentioning again. You can use a sharpening stone or invest in an electric sharpener. They are not very expensive and take up very little storage space. Make certain you purchase one that is appropriate for the types of knives you own.