An apartment with a fully functional kitchen is definitely a must. To me, there are few things more satisfying than hitting the local market, finding everything you need for dinner, purchasing all of it in a foreign language (or a ton of hand gestures and the appropriate greetings and gratitudes in the native tongue) and walking back to your apartment to cook it and enjoy it on a balcony overlooking a foreign city you are just getting to know.
I have also have grown fond of returning to my temporary apartment in the afternoon for a short break from exploring; when it's too hot, or when the city becomes a touch overwhelming (I'm thinking of you, Moroccan medina!), it's incredibly restful to come back to a place where you feel completely at home, even though you are hundreds of miles from your own. Even daily chores become relaxing whilst on vacation; I have only recently discovered the joy of hanging the laundry on the clothesline as I listen to neighbours chatting in a foreign language (though I am positive that to many of you, this sounds absurd!)
Though it had everything we needed and more, it was the character and soul of the apartment that truly blew me away; I felt connected to it in a way I can't explain. I knew it would be perfect the moment I set foot inside. The owner, the loveliest Belgian woman, told us it had been abandoned for 70 years before she purchased it. Much of the original charms have been preserved and everything was just right in every way; the windows, the breeze, the light...