I've got two mature ones in the "pretty" gardens up by the house. They have both tended to have very sparse, open canopies and a habit of dropping branches, so I never really did anything to them.
Until we had a hellacious windstorm right before new year's. Two straight days of gale easterlies, including most of a day out of the NE, which is a quarter we rarely see any wind come from. The bigger tree got wrenched out of the ground and tossed in a heap. I wasn't prepared to write it off completely, since it was the kids' swing and climbing tree, so I cut it back to just the trunk, and used a block and tackle plus a hi-lift and some stout timber props to hoist it back up to something resembling vertical.
[edit to add] For an idea of the physics involved in how this tree went down, the direction of the fall is directly into the strongest winds. This is a really sheltered spot, with tall trees all around, so I can only imagine how some combination of turbulence and possibly a few intense downdrafts must have twisted the crown and uncrewed the base of the tree from the ground.
After bucking, splitting, and stacking, I estimated half a cube of firewood for my time and trouble. It's a dense wood, like lots of legumes, so I expect it will have a lot of heat value. Really attractive colouring and figure, too...reminiscent of mesquite and Tasmanian blackwood. The tree started putting out new growth within a month and now has a few clusters of shoots. It's dropped most of its leaves now and gone dormant for the winter, so I'll keep my fingers crossed for a resurgence in the spring. There's a big dead/rotting strip running up one side of the trunk, so it might be on borrowed time anyway. If that's the case, I have allowed one root sucker to come up and if the original stem packs it in, there's a replacement right next to it.