During the years that we lived in an apartment with this tiny kitchen, we cooked as much as ever. What was the difference between using such a small kitchen versus a larger one? The range of small "convenience" appliances was probably more akin to that of our grandmother's generation than of present day norms: We're not going to recommend against the obvious here, like ice shavers and bread makers. Instead, these are five very common small appliances that we found we didn't really need when pared down in a small kitchen. Your list may vary based upon preferences and repertoire, but here's ours:
Stand or Hand Mixer: A stand mixer would simply not be comfortable in such a small kitchen, and without it we found we didn't really need to have a hand mixer either. Mixing by hand, of course, is far more difficult, but it was done for ages before us and it takes absolutely no storage space. Plus, there are some recipes where we could swear that it yields a better result than electric mixers.
Food Processor: Like above, we are the only food processor in our home.
Electric Can Opener: A simple little metal one with two more fittings for bottle caps and popping the tops off of homemade canned goods suited us well.
Microwave: The tradeoff for living in such a small apartment was being right in the middle of a neighborhood filled with markets and grocery stores. Cooking fresh from ingredients picked up on the walk home from work meant no microwave dinners. And leftovers, when we had them, were heated up in the office microwave for lunch at work! So, though we had a microwave in the pantry, we rarely used it.
Toaster: And we love toast. But the oven does the job just fine.
The funny thing is, living without these five appliances informed our cooking habits to the point where we still don't use most of them - even in a larger kitchen. We have yet to own a stand mixer and we find hand mixers downright clumsy, so manpower mixer we remain. That same little metal can opener works better than an electric space-hog and the poor toaster hardly ever sees the light of day. A food processor has yet to grace the countertop and the microwave is pretty much just a giant nut toaster (we really should get rid of that thing!).
All of that said, there's one small appliance we found invaluable in a tiny kitchen (or any kitchen, for that matter): The immersion blender. It stores away like it's nothing and it gets heavy use in a home of soup-and-smoothie lovers.
What are the common small appliances that you've found you simply don't need (or what are those that are an absolute must)?