A surprisingly prevalent myth that surrounds Galileo is the reason for his blindness. It has been documented in magazines, newspapers and many websites that Galileo went blind in one eye after observing the Sun through his telescope. This is nothing but an urban legend.
It is a known fact that Galileo was the first person to use the instrument, we now commonly refer to as the telescope, for astronomical observations. He was one of the first person to observe and state that the Moon is not blemish free and that it has a lot of hills and craters and other uneven features on its surface. Galileo was also the first to observe four small “spots” around Jupiter and correctly interpreted them as Jovian moons. Till date these four satellites, Io, Europa, Gynameade and Callisto are referred to as Galilean Moons.
Galileo did observe the Sun using his telescope, but did so when the Sun was almost on the horizon at sunrise and sunset. This was around the year 1612 (at the age of 48). Soon he discovered the projection technique and started detailed solar observations using this technique. After a year of him observing the Sun, Galileo documented numerous drawings of Jupiter and its four satellites. This could not have been possible if Galileo had lost his sight while observing the Sun.
According to most sources Galileo turned blind almost a quarter century later, at the age of 72 and the most probable cause was cataract and glaucoma. There are proofs of Galileo reading his renunciation at his inquisition (when he was charged by the church) at the age of 70. His eyesight must have been good at his point and hence solar observations could not have been a cause for his blindness.
Incidentally, even after losing one eye due to cataract he took excellent observations of the Moon and discovered the lunar liberation phenomenon.
Thus Galileo was well aware of the dangers of direct solar observations and seems to have predominantly used the projection technique after initially observing at sunrise and sunset. Solar observation is indeed very dangerous if not carried under extreme care and expert supervision. It will cause blindness if care is not taken, but as far as Galileo goes, he was smart and careful enough.