Mesquites ! Wonderful shade but they cause such a mess.

salt cedars!!!!! my neigbor has one and they are a pain to my pool plus they emit salt which basically make the ground around them baren. and not a tree but bouganvillas are also a mess

Well just about every tree makes a little mess... it really depends on where it is and whether you prefer mass fall leaf drop or constant small dropping.

Pine trees I could not deal with, but I have a native (velvet?) mesquite over dirt that doesn't produce much litter. If a tree has flowers, they are going to drop at some point.

As far as "trash trees" go the one that comes to mind is Jerusalem Thorn (aka Mexican Palo Verde). They are far messier than any of my other trees. Agree that salt cedar is incredibly messy. Have heard mimosa is in the trash tree category.

You'll also have bean pods with a lot of desert adapted trees... some of them are edible, if that interests you.