I’ve been a happy user of MailStore Home for years. It lets me easily archive mail off of my various email accounts, store it locally, and still easily search it all. (I’m probably paranoid, but I don’t like having years of my personal emails stored on free email services.)
Due to some security changes and lack of support from MailStore, my Outlook.com accounts no longer work with their tool. It’s hard to complain too much when I’m using a free tool. They make their money from corporate customers. So I was off to search for something else.
There are lots of other options, but I kept seeing people recommend Thunderbird which is the email client from the Mozilla Foundation (makers of the Firefox browser.) I was able to export all my emails from MailStore to EML files and then import them into Thunderbird. It will take me a while to get used to the search interface, but functionally I’m back on track. I don’t like the interface enough to switch from my regular email client to just using Thunderbird, but it’s easy enough to open Thunderbird every once in a while and archive some emails from my various accounts to my local folders.
So if I’ve previously recommended MailStore to you as a way to archive your email locally, my new recommendation is Thunderbird. It’s a nice way to have access to all my old emails without letting companies scrape through my content. If you don’t care about that and if you don’t run out of space on your free email accounts, then you can ignore all this.