Storyboarding (if any): I use yED for my puzzle-dependency charts, as well as notepad and Microsoft Word for writing down the basic plot and any ideas I might have.
Paint Backgrounds: Paint.NET.
Make Sprites: Paint.NET
Make Animations: Paint.NET, sometimes Asesprite to help with the visualisation.
Sound Effects: I either use Bfxr and edit it slightly with Audacity, or I simply record something straight onto Audacity
Music: I've got this brilliant midi music generator called Diatonic Composer, which I usually use to make my music before I edit it slightly using Anvil Studio.