Can one build a laser using spontaneous emission? We use stimulated emission and not spontaneous emission to produce lasers. Why is this? Can't we produce lasers by the spontaneous emission method?
 A: spontaneous emission occurs in all directions, and is akin to a glow. to have a concentrated beam with low divergence (that's the idea of a laser), the photons must all be moving in the same direction--that's where a pair of mirrors come in. the high concentration of photons on this axis directly increases the rate of stimulated emission too. but spontaneous emission cannot be increased so simply--that's why it constitutes only about 1/10th of the output radiation of a typical laser .
A: Actually we do use spontaneous emission to build a laser. A laser pulse begins as spontaneous emission. As the spontaneous emission travels through the gain medium, relatively coherent stimulated emission joins the pulse. 
Spontaneous emission can have a wide wavelength spread - it's wavelength is not simply the zero uncertainty value implied by the $h\,\Delta \nu$ step between atom energy eigenstates. The emitting atom is coupled to all modes of the quantized electromagnetic field, so there is a range of wavelengths it can emit in. This is the same mechanism that begets the Lamb shift between otherwise degenerate eigenstates of e.g. the Hydrogen atom as reckoned by the Dirac equation. Also, especially  in gas lasers, spontaneous emission wavelengths are further broadened by Doppler shifting.
See for more details my answer to "Why do lasers require mirror at the ends?".
Therefore the total radiation can in principle be quite broadband  - comprising little coherent contributing pulses. It is the purpose of the resonant cavity to (i) raise the probability of stimulated emission by recirculating light several times before output and (ii) cull pulses not at the cavity's resonant frequency before they build up and waste too much of the stored energy in the population inversion. 
None of this would be a problem if we could ensure that the whole laser pulse began as one spontaneously emitted photon. But this is not the practical situation - there is a great deal of engineering needed to make laser outputs stable and narrowband.
A: Spontaneous emission is random in direction and incoherent. Consider an LED for example.
Laser light, by definition is a coherent source of light where all photons have the same phase, frequency, polarization, and direction of travel. Secondly, as opposed to spontaneous emission, stimulated emission causes an increase in the photon number as light interacts with atoms in the medium, and when population inversion occurs (i.e., the rate of stimulated emission exceeds that of absorption in the medium), this leads to optical amplification. Hence, "Light Amplification by Stimulated Emission of Radiation" LASER. 
