Turns out that regionally, people think of one of three different creatures when they hear the term "Daddy Longlegs":

1. The "official" Daddy Longlegs, also known as "Harvestmen" or scientifically an "opiliones":
   
   
    
2. The "Daddy Longlegs Spider", also known as a Cellar Spider:
   
   
    
3. A "Crane Fly", also known as Mosquito Hawks or Giant Mosquitos:
   
   

And just to freak you out, enjoy this: