Laika was launched into orbit with the Sputnik 2 rocket in 1957. [nasa.gov]
Country: the Soviet Union, China
The Soviet Union used pairs of stray female dogs in its early space experiments in the 1950s and 1960s; most of those flights were successful, and some dogs flew more than once. On July 22, 1951, the Soviet Union launched the R-1 IIIA-1 flight, carrying the dogs Tsygan and Dezik into space. The dogs became the first higher organisms to be recovered alive from a spaceflight.
Laika, the most famous canine cosmonaut, followed Tsygan and Dezik into space aboard Sputnik 2 on November 2, 1957. Laika, a former stray dog from Moscow became the first living being to orbit the Earth aboard Sputnik.
On August 19, 1960, Sputnik 5 (also known as Korabl-Sputnik 2) carried the dogs Belka and Strelka. It was the first spacecraft to carry animals into orbit and return them alive. Following this, in February 1966, a further two Russian canine cosmonauts named Veterok and Ugolyok travelled aboard Cosmos 110 and spent 22 days in orbit.
In July 1966, two Chinese dogs named Xiaobao and Shanshan also became space astronauts when they left Earth aboard the biological rocket T-7AS2.