I have a lot of saved web pages that I want to view whenever I want without the page connecting to the web site (I can do this on WM). How do I do this on Android? Every time I click on the HTML file it says "no connection".
Save the pages with an instapaper client Save to instapaper.
Another way would be to use Read it Later ($1) or Instapaper (as suggested by Edelcom) to save something from your desktop for offline reading on your mobile. Though I've not used it myself, iPaper looks to be a decent client for Instapaper.
You can use OffLine Browser by Nikodroid. It can save web pages (and related links) and then allows you to read them when you are offline.
You could also generate PDF files using the share feature of the Android system. I am currently researching the best way. For now I am using Web2PDF with Chrome on my Nexus 10. Does not work perfectly with all sites though. For those that do no work yet I am using the website PDFmyURL.com.
Today I noticed hat Firefox can save PDF of whole pages by default. It is hidden in Extras...
You can use PaperSpan app to save original page offline to SD Card. Saving links can be done through computer, and app will sync and save offline.