We've found the following kitchen appliances to be indispensible to our kitchen:
There's nothing like eating fresh bread right out of the oven. But it can be a big hassle if you don't have enough counter space to knead-knead-knead that dough. While it will require a chunk of usable counter space, the bread machine is vital to our small kitchen gourmet.
If you happen to have only a two-burner stove, a rice cooker can be a life-saver. It frees up a burner, so you can cook your main dishes and still have a lovely rice side dish.
Our waffle baker is one of those models which converts to a flat griddle. It's really handy because it cooks twice as many pancakes than in a regular skillet, and we can use it at the kitchen table. No one has to be stuck in the kitchen flipping flap-jacks anymore!
We use our blender at least every other day it seems. Sauce too lumpy? Run it through the blender. Need a quick salad dressing? Throw some oil, vinegar, and herbs into the blender. It's definitely indispensable.
The microwave is definitely a useful appliance to have in the kitchen. Ours is on top of our refrigerator so it doesn't take up any counter space. Re-heating, pre-cooking, and heating water and milk for tea and cocoa are some of its indispensible uses in our apartment.
Our KitchenAid mixer has proven to be pretty handy for whipping up cake mixes and brownies for that last minute dessert. But it does hog some counter space, so it's pretty much a trade-off. We've often thought a hand-held model would probably be better for our needs, but someday we'll have a bigger kitchen.....
A crock pot is really nice for those "throw it in the pot, turn it on, and leave it" meals. Soups, stews, etc. come out so tasty when they can slow cook. Once again, though, it takes up storage space in a cupboard.
Need we say more? There are times when even a Small Kitchen Gourmet meal seems to use every pan in the house, and who wants to wash those by hand? If you happen to have a dishwasher, you are fortunate indeed...