In New Mexico, disease pressure is minimal. Apricot, apple, pear, and peach trees thrive with no special attention. Plums and cherries sometimes get canker, etc. Late spring freezes are the main danger to good crops from any of these. Mulberries and jujube are two that come out of dormancy late enough to fruit consistently every year.

Plum trees here have little/no problem with diseases, it's the insect pests that are the main destructive force (trunk borers and plum curculio). The least problem fruit tree for avoiding both diseases and pests that I grow is my Japanese persimmon tree.

My Asian persimmons do not need spraying for bugs or disease at all. Now, you didn't mention squirrels, possoms, raccoons.

Dave, oddly my Asian persimmons are totally ignored by squirrels and birds, and thankfully possoms and raccoons are scarce around here. The few persimmons which are left over at the top of the tree (can't be reached for harvest) do get the birds interested but only after they turn mushy. And you are so right about caring for this tree, no sprays required, plus little if any pruning too. Here's mine at age 15 years (pic from last Sept)...

Just curious: since the vgkg tree has fruit too high for harvest, how was the tree photographed from above?

The tree's trunk is visibly planted firmly in the ground on which I was standing upon. If I were in the picture my head would be level with the flag on the left. The tree is about 12' tall and and the ripened P fruit is not easy to let go, like a ripe plum or pear would. I use a small pruning sheer sniping off each fruit to avoid damaging next year's bud stem. Here's the result...

...or rather about 1/3 of them.

To fully answer matthias_lang original question, after Persimmons, my other #2 and #3 top care free (and disease free) fruit trees would be Pears and Figs. The fruit trees which need the most care here are all in the pitted family.

Duh. I mistook the top of the picture for the top of the tree.

Upper midwest. Plums and cherries - although the birds are pretty good at stealing the cherries.

Do nuts count as fruit in this case?

My healthiest tree here is a macadamia.

My mulberry tree comes back to life so late every year I wonder if its dead.

Sour cherry trees and pear trees do the best here. Still waiting on my persimmon to bear fruit. Not even sure if it's still alive but its dark out there now.

Figs, plums, and bush cherries (ie Carmine Jewel, Romeo, Juliet) have not needed spraying. So far nothing has attacked my pears or manchurian apricot, either, although that manchurian apricot blooms far too early to get fruit (so far). I have to spray for peach leaf curl on the peach, and for scab and fireblight on the apples.

Since Plums do well, you should also try Pluot and Aprium.. they have been trouble free (no spray) for me.

@Granite City Services

What kind of mulberry is that? My mulberries are worse than my average fruit species in terms of getting damaged by late spring frosts. Or maybe it's just a difference in our locations?

Rabbiteye blueberries are very reliable in my zone 7 NC location. They have no major disease problems, often little to no insect problems, especially not on the early (late June/early July) ripening varieties, birds bother them very little (although I have friends that live in a nearby city for whom birds are a significant problem), and although they bloom early and are often exposed to temperatures in the 20's, sometimes well down into the 20's, after beginning to bloom, I get a good crop almost every year, and even in the worst year I've still had an okay crop.

And what others have said about how trouble-free Asian persimmons is true for me, too. And American persimmons, too.

Muscadines are very reliable with very few issues.

My satsuma is super reliable, although it tends to alternate between big crops and smaller crops, and I have to cover it on the coldest winter nights, because it's not hardy enough to grow here unprotected.

Those are some of the woody, fruiting plants that come to mind in terms of reliability.