According to this Huffington Post article,
On Thursday, Amazon began offering free same-day delivery to Prime members in 14 metro areas across the country: Atlanta, Baltimore, Boston, Dallas-Fort Worth, Indianapolis, Los Angeles, New York, Philadelphia, Phoenix, the San Francisco Bay (including Oakland), Seattle-Tacoma, Washington, D.C., San Diego and the Tampa Bay.
Same-day delivery used to cost Prime members an extra $5.99 per order. To qualify for free same-day delivery, you must place an order before noon and spend at least $35.
It will be very interesting to see how this play out in the spreading metropolitan in US. The main issue is the economics of delivering cost and how to make it scale.