Hard copy -- I'm embarrassed to say I just scribble my notes on whatever is near me. And then I inevitably fail to find them when I need them.
Spreadsheet (Numbers, since I'm on a Mac):
Planning and world-building notes. This includes power progression mapped to major book events, as well as races, gods, locations and distances, character names, descriptions, travel speed for different modes of travel, notes on different accents, types of magic, treasure shares, timelines, and recruitment budgets (for when the main characters need to hire people).
Major story beats separated out by book, with any writing notes that occur to me that should be associated with each one. As I work my way through the series, each of these sections is then fleshed out in more detail with minor story beats and more ideas for scenes and events.
Scrivener (which is also where I do my writing):
1. Scene and PoV notes. For each batch of chapters (I usually write three chapters at a time), I take my notes from the text editor above and split that out into ideas for which scenes need to occur, and which PoV will be used for each scene. That goes in Scrivener's "Binder", as the label for each individual scene ("PoV Character: brief summary of scene").
2. In Scrivener's "Notes" area for each scene, I transfer certain writing notes from the text editor if I think I'll need the reminders about what I wanted to include in the scene. I also add any other reminders I think will be helpful, like the list of characters who are currently present (so I don't mention someone who's not actually there), or sections copied from earlier scenes with character descriptions or dialogue that models someone's accent, to make it easier to stay consistent without constantly flipping through earlier scenes.
3. Also in Scrivener's "Notes" area for each scene, I keep a record of anything I delete from the scene, in case I want to reference it or add it back in somewhere else.
In all seriousness, I've recently switched to Scrivener for organization along with the writing itself, so that's been working out a lot better than my various previous attempts at organization. Oh, I also used to use Trello as well. Sometimes I still use it since it has a mobile option while Scrivener doesn't.
For ideas that might become stories, I use Google Docs.
I store my maps in Google Docs.
I do all of my writing in Google Docs.
For meta-knowledge about my world that I know (but only hint about in my stories) I use Google Docs.
When I absolutely need to jot down some utterly urgent notes for a story idea, I'll open up Google Docs.
I've considered breaking the corporate chains and learning Emacs for Org Mode, but I've never quite screwed my courage up to the sticking point and dived into the whole 'real text editor' mess.
On the one hand, it's cross-platform, free, and super duper powerful.
On the other hand, it's basically a whole OS + programming language, and that just sounds like a huge distraction - and not even a super fun one.
Then for the chapter and scene brainstorming and working out problems I have a physical notebook. There's just something about paper. I used moleskine expanded edition, because it's 400 pages thick and I like the way it feels. I also like that I have mine without lines so that I can write bigger or smaller or draw things out if I feel excited. :D I ramble my way out of problems in there. When I found a solution or a cool idea comes up I highlight it so that I can find it easier later in the mess haha.