For the paperwork: file cabinets with hanging folders. We have one set for my husband (bills, receipts, warranties, etc.). For me, we have another set where I file recipes, craft project instructions, my writing, and other paperwork type things.
For crafts/toys: We went to Lowe's and bought two 9 cube organizers that each have a spot to hold a one foot by one foot (maybe 18 inches, but it's a decent size, either way) fabric cube. Or you can forget the actual cubes and use the space for your own organizing container, but the cubes are kinda nice to have. One set of cubes is actually for small kids toys. We have four children, and they each have their own cube to throw their special things into. The rest hold things like action figures, light building toys, etc. This has helped tremendously. The other cube is being used for crafts. I only have four of the fabric cubes in that one. One holds papers to be filed that I don't want sitting out getting scattered. One holds small to medium sized gift bags. Another holds tissue paper, bows, and name tags. I can't remember what I put in the other off the top of my head, but you get the point. I also bought two plastic containers (not expensive, from Walmart) that can fit neatly in the cube holder. One is a set of three smallish drawers that I use for pencils, pens, crayons, and markers (this has been the best thing ever!); the other is just a small tub with a snap on lid that holds stapler, water colors, paint brushes, glue, and other things that I want to be able to carry around yet keep contained when not in use. I'm planning on getting another of these so I can sort a little bit more.
For finished paperwork or crafts: I have some that I keep in a big plastic tub under my bed. I have others that I just take a picture of for a way to "keep" it, and then toss it. Workbooks go on the kids' bookshelf if they're still in use. Otherwise, they go in the trash.
Christmas/birthday presents: I'm sorry to say, we just chuck them up in the top of our closet until we need them. Probably not the best system, and I'm sure our kids will catch on sooner rather than later, but it's the only spot no one really pays attention to at present.