My system is a hodge podge of old school methods and current tech.
You Need a Budget app for tracking expenditures and then every month it's reconciled with our various credit card/bank accounts. I try to enter receipts the same day as a purchase, everything has a category. If there are more complicated financial things to track, I stick to Excel.
I have a big dry erase board that I made into a calendar grid, I think it's about 2' x 3'. I see each month's appointments and activities, we have 4 people and a dog in our household, everyone/pet gets a different colored dry erase marker for their events. I also use Google Calendar but prefer the visual reminders right above my desktop monitor.
I use a physical annual planner for everything else, especially if I'm not in front of the dry erase board. I bought the latest one at Home Goods. Yes, sometimes have to do write things twice in my planner and on the big calendar but most of the time these things get etched on my brain and I usually remember them independently as a result.
I have DropBox and Evernote set up on my computers/phones for keeping track of other random things (taste testing notes for food/drinks we've tried, projects for our hobbies, things I want to buy, etc.) I occasionally use Pinterest.
I love our Fujitsu ScanSnap document scanner for items where I want to keep digital records but don't need a physical copy. For example, every couple of weeks I scan the highlights of our kids' art creations from school. I save maybe one or two great drawings and toss the rest after they're digitized. My son (almost 6) is a very prolific artist and being able to see the progression of his skills at this age is really cool.
My husband and I share a 5 year daily journal, we each write a couple of sentences at the end of the night about what happened that day. I love being able to read previous years entries every day on the same page. I have an 18 year weekend journal that I have not been as good about updating. The idea behind that book was to write about things that you do with your kids every weekend, until they're 18. You can find both of these type of journals on Amazon.