Problem: I have a Galaxy S4 and at some point it decided that when I press the home button on the phone it would always open up the recent apps window - even if I didn't hold the home button down! This got frustrating but I started adapting to double-hitting the home button all the time.
Resolution: Found out when working on my wife's phone - this started happening to her after installing the Dolphin browser. So I fiddled with it and I figured it out - Dolphin's "Confirm before exit" setting was causing it, turn that sucker off and restart your phone!
TL;DR/To fix - open Dolphin, go to Settings, then Exit Settings, then turn off the "Confirm Before Exiting" setting. Restart your phone and BOOM. Worked for me. Others have also mentioned that they noticed this happening when using the Samsung Keyboard or the Samsung preinstalled Swype instead of the Google keyboard or the full Swype+Dragon app.