What observation led bohr to believe that electrons had certain, finite, discrete, exact amounts of energies and thus were on quantized energy levels?

The release of light energy in packets or quanta by electrons.

Bohr discovered the following:
1. Electrons move around the nucleus in prescribed orbits.
2. When an electron jumps from an orbit with higher energy to another orbit with lower energy, the electron emits a discrete, exact amount of light energy (or a quantum of energy).
3. Boh's discovery led to the development of quantum mechanics, which defines energy release in quanta or packets, at defined frequencies and wavelengths.