Answer to
What was the first single launch to put two or more independent payloads into Earth orbit?
update: The Washington Post says it's probably this one, confirming @JoeJobs' answer as well.
above: image of the Thusrday, June 23, 1960 Washington Post article "Piggy-Back Satellites Hailed As Big Space Gain for U.S." found here: https://web.archive.org/web/20070726215210/http://www.ncst.nrl.navy.mil/HomePage/GRAB/GRAB_Photos.html
New Space First
The feat of putting up a pair of satellites simultaneously with a single booster was a new space “first” for the United States. This has not been attempted, so far as it is known, by Russia.
A two-stage, Thor-able-star, an Air Force Rocket, accomplished the feat.
The Transit II-A satellite, the navigation aide and time-measuring sphere, soared into a near-circular orbit that wil carry it over all of the Earth’s land masses — including Russia — except certain Arctic and antarctic points.
Original answer, kept for its archival value:
I can't be sure this is the first attempt, but it might be the strangest-looking: GRAB + ELINT. However it was unsuccessful, and in a very big way.
Taken from this answer:
The item on top is called GRAB 1 for Galactic Radiation and Background. However that's a cover:
Galactic Radiation and Background (GRAB) was the covername for Project Dyno ELINT intelligence satellites operated by the U.S. Naval Research Laboratory (NRL) shortly after the Cold War U-2 incident of 1960. The satellites carried two sets of instruments: an unclassified experiment (called Solrad) and a then-classified payload to collect electronic intelligence (ELINT) (called Tattletale). Of five attempted launches, two missions were successful. The program is also known by the later codeword Canes.
Reading further:
Incidents
During the second launch attempt, the Thor booster shut down 12 seconds early, and the flight was subsequently terminated by Range safety. As fragments fell on Cuba, subsequent launches from Cape Canaveral flew a dogleg trajectory to reach 70 degree inclination.
I'm not yet sure if this is the origin of doglegging to orbit, so I've asked Which launch was the first to use a dogleg maneuver?