I had a white birch that was close to my pool several years back that was a mess and was constantly clogging up my skimmer basket. I could not leave my pump running when I wasn't home for fear of burning up my pump due to lack of water flow. Thankfully, it was also too close to a power line so the power company cut it down at their expense.

I also had a crabapple tree by my pool deck and crabapples were always dropping in my pool. But, the huge derecho storm we had here in June of last year took that tree down. (Along with power to 80% of all the people in the state for a week and we had temps in the 100 degree range that week. Having a pool was the only thing that made that week bearable. I couldn't run the pump so couldn't clean it but poured in bleach and, though the floor was dirty, the water stayed clear.)

(I know Ben hates them, but I have a couple of Crepe Myrtle trees in my front yard and I love 'em!)