How many PLANETS were discovered without 

6 Planets - Mercury, Venus, Earth, Mars, Jupiter and Saturn were discovered without using any telescope. Exact source is there discoveries are unknown as they were visible in night sky if anyone carefully observes them. Last three planets Uranus, Neptune and Pluto were discovered in 19th and 20th century using telescopes. If you are interested in the knowledge of space, stars and planets then the historical facts about discovery of these planets with naked eye might surprise you.

Today nobody would like to search for planets in the sky without a powerful telescope. But there was a time when there was no telescope but curiosity to find something special in the sky. People tried to calculate future by looking at the positions of stars in the night sky. In order to do so, some ancient astrologers and mathematicians discovered the planets without any powerful equipment to do that.

History of Discovery of First Six Planets of Solar System

• Around 2nd millennium BC, Mercury, Venus, Mars, Jupiter and Saturn were identified by ancient Babylonian astronomers.
• Greek philosophers Philolaus and Hicetas (in 5th Century BC) speculated that Earth is a spherical object revolving on some mystical axis “central fire” that regulated the universe.
• In Ancient Greece (till 2nd Century BC), Earth was believed to be the center of complete universe. All stars and other celestial structure were believed to be orbiting around the earth. Moon, Mercury, Venus, Sun, Mars, Jupiter and Saturn were considered as planets (in order with increasing distance).
• Anaxagoras (around 450 BC) proposed that the Sun is a star.
• Aristarchus of Samos (around 3rd Century BC) said that Earth and other planets moved around Sun. He replaced the idea of "central fire" with Sun. His belief was not widely accepted till 17th century.
• Nicolaus Copernicus (in 1543) proposed the planetary system where Sun was not considered as a planet, but as a star sitting at the center with other planets revolving around it. 

Nobody know the names of  Babylonian astronomers who discovered these planets, but their discovery was widely used in other civilizations as well. Babylonian astronomers were know for their scientific approach and mathematical calculations in predicting events.

I have myself tried to look at sky in search of planets without using any telescope, but can't go beyond Venus and Mars. Even my 30x Optical Zoom DSLR camera gave a very slight view of Saturn, only when i previously knew that it is Saturn. It was certainly an achievement of those ancient astronomers who found these planets with their will power, and yet we don't know their names.