Scrapbook (Firefox)
This extension is quite famous, it has even got a Wikipedia entry. The following description is from Firefox add-ons:
ScrapBook is a Firefox extension, which helps you to save Web pages
and easily manage collections. Key features are lightness, speed,
accuracy and multi-language support. Major features are:
- Save Web page
- Save snippet of Web page
- Save Web site
- Organize the collection in the same way as Bookmarks
- Full text search and quick filtering search of the collection
- Editing of the collected Web page
- Text/HTML edit feature resembling Opera's Notes

Scrapbook (Chrome)
This one is from a different author, but it mimics most of the functionalities:
Features
- No service to subscribe to, total privacy to store your annotations. Simple SQL based webstorage at backend.
- Easy folder based access right from the extension's pop up. The storage is completely offline.
- Undo and remove. Add Sticky Notes to pages.
- Deletion of pages is supported.
- Easy management using the options menu.

Pocket (Offline mode available only on Chrome)
Pocket is an online bookmarking service which was previously known as Read It Later. It can be used to bookmark and sync links across devices, including Android and iOS smartphones. It features browser extensions for Firefox and Chrome, however those are only useful to save articles, not to read them.
On Chrome, you can install the official Pocket app (different from the Pocket extension) that works offline:
What can I save?
Save articles, videos, recipes, and webpages you find
online or from your favorite apps.
View everywhere, even offline
If it’s in Pocket, it’s on your phone, tablet or computer, even when
you’re offline. Perfect for commutes, travel, and curling up on your
couch.
Better viewing experience
See your saved items in a simple,
easy-to-view layout that improves the viewing experience of any page.
Works offline
Access what you’ve saved offline. Set up Pocket to only
download when connected to Wi-Fi to reduce data usage.
