Several apps are available for storing and reading web content offline, Instapaper and ReadItLater being two of the more popular ones. I have tried both and prefer ReadItLater because I like how it displays content. ReadItLater just recently became available for Android, and the Pro version costs $2.99. If you just want try ReadItLater out, you can now install ReadItLater Free on Android phones.
The free version does have a limit on the number of articles that you can view or download, so it is most useful for checking the app out, as opposed to other free, ad-supported Android apps that provide all of the features as paid version but display advertisements. You also cannot search or sort your reading list.
If you are not familiar with ReadItLater, it is a service that works best in combination with PC web browsers and iPhone, iPad, and Android apps. When I find a web article while browsing the web from my PC that I want to save to read at another time, I click the Read It Later button on the browser’s toolbar. Next, when I am ready to read items that I save, I start the ReadItLater app on my mobile devices, which by default displays the content in a text mode that optimizes the content for display on the mobile device’s screen, although you can see the full web version as well.