Hoardy-Web by Jan Malakhovski

Hoardy-Web (also there) helps you to passively capture, archive, and hoard your web browsing history.
Not just the URLs, but also the contents and the requisite resources (images, media, CSS, fonts, etc) of the pages you visit.
Not just the last 3 months, but from the beginning of time you start using it.

Practically speaking, you install this and just browse the web normally while Hoardy-Web passively, in background, captures and archives web pages you visit for later offline viewing, mirroring, and/or indexing.
Hoardy-Web has a lot of configuration options to help you tweak what should or should not be archived and a very low memory footprint, keeping you browsing experience snappy even on ancient hardware (unless explicitly configured otherwise to, e.g., minimize writes to disk instead).

In other words, this extension implements an in-browser half of your own personal private passive Wayback Machine that archives everything you see, including HTTP POST requests and responses (e.g. answer pages of web search engines), as well as most other HTTP-level data (AJAX/JSON RPC/etc).

By default, this extension will save all captured data into browser's local storage, so it can be used standalone, but it implements other archiving methods if you want them.
To view/replay your archived data, however, you will need to install at the very least the accompanying hoardy-web tool (also there).

If you do not care about archival, you can also use this extension to log and later inspect HTTP traffic generated by various sleazy websites, even when they generate said web traffic on events that can not normally be inspected with browser's own Network Monitor (e.g. when a page generates HTTP requests when its window closes).

For more information see the built-in Help page (available via the "Help" button from extension's popup) and project's documentation (also there).
The latter page also contains in-depth comparisons to DownloadNet, mitmproxy, archiveweb.page, and other similar and related software.

- Hoardy-Web DOES NOT send any of your captured web browsing data anywhere, unless you explicitly configure it to do so.
- Hoardy-Web DOES NOT send any telemetry anywhere.
- Both of the above statements will apply to all future versions of Hoardy-Web.

Hoardy-Web was previously known as "Personal Private Passive Web Archive" aka pWebArc.