Asia (The Economist; paid subscription required to access fulltext)
Asia Today (The Asia Society)
Himal (Nepal/South Asia)
South Asia Monitor (Center for Strategic and International Studies)
Annotated guide to Afghanistan news sources
Holiday (newsweekly)
Annotated guide to Bangaldesh news sources
Outlook (recommended)
Friday Times (recommended; paid subscription required)
Annotated guide to Sri Lanka news sources
Further News Resources (from The Guardian)