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For the goal of not losing them, consider hosting your papers on Dropbox, version control (such as GitHub, private repos are gratis now) and/or on Overleaf.com (nice in-browser editor with real-time collaboration; can also edit offline with your favourite local editor but may need paid account)
Authorea is close to what you want — it renders to html (but supports latex/pdf export), supports latex & markdown, and is git-based (not yet exposed in a friendly way).
@Lierre: way less of an issue than giving the paper copyright for free to publishers who put it behind a paywall, which is still the norm for most scientists :-(
