That's a little complicated of a question, especially as I am not sure I could definitively define what fruits are my "favorites"
Obviously the answer is "no" for anything tropical or semi-tropical (so no lichi trees, guanabanas, cherimoyas, uglifruit, and so on)
Theoretically I am in a climate to grow a few ones I like , like mirabelles, "classic" greengages, a good yuzu (theoretically, they're good to about -5 or 10 below C so I'd probably have to wrap it in the winter and hope for the best) and the apple I call the Szechuan Snowball (a very sweet, nearly dead white skinned apple I bumped into at the Ag experiment station at Geneva in my Cornell days.) The problem however would be space, we don't have any (nearly every inch of our property that isn't covered by the house is shaded by the natural trees, which we aren't allowed to do anything to by Village ordinance, especially for anything that would need two or more trees to set fruit. For a lot of them there would also be the trickiness of getting my hands on the "correct" one (the strains of yuzu, green gage and such things I like are very rarely the same as the most common and popular ones, and a lot of places don't really bother to specify variety with what they consider "niche" fruit.) and propagating them (I could simply write to Geneva to get a sample of the apple no problem, but it would be a bud scion they sent me, and my track record at successfully grafting is more or less zero.) and time (there's really little point in putting in a fruit tree that will take ten or more years to really get going, since who knows if I'll be living here by then.)
Outside of the weedy wine berries (which grow of their own accord) and some very rickety blueberry bushes (invariably devoured by the birds) the only two fruits I have ever actually grown are a peach tree and some strawberries. The peach tree was in fact an ornamental/ rootstock one called a Hiawatha (purple leaves) but it did make peaches that while tiny (golf ball sized) and rather sour, were edible (at least for the first few years, after that, the tree was big enough that the chipmunks and squirrels could reach and devour every last fruit long before they were ripe.) That tree conked out about two or three years ago (a combination of running out of room and some very cold winters)
The strawberries actually did very well for the years they were there. They were Alpine Whites, and it turns out birds don't usually go after white strawberries (maybe they can't recognize them as ripe) It also probably didn't hurt that the pot they were planted in also was home to a very large hive of sweat bees which, while harmless to me, were probably a great anti critter defense (as well as an excellent source of pollinators.) Alas eventually we got a winter that was so cold and so long it proved too much for even them, and they never came back. May have to try them again someday (I have also heard tell of a green fruited form of one of the European strawberries, that sounds fun too.)
I also have off and on plans involving some dried apricots I think are Hunza as opposed to the standard. Those theoretically might be able to take the cold here (the Hunza valley is afer all by the Himalayas) and unlike normal plum and apricot seeds, they don't need vernalization (so I don't have to leave the pits outside over the winter to get dug up and eaten by the animals. If I could be a pretty fun type of tree (I don't much care for dried hunzas but maybe they are tastier fresh) And since Hunza's are sweet pit (low cyanide) I basically would get almonds out of the deal too!
. She just allowed me to indulge myself in the spirit of adventure. Although not a large garden, we, Mom and I, had lots and lots. I could use my special belt buckle both as a knife and a spoon 
