The most used oscillator type in microcontrollers is the pierce oscillator, Abracon introduces you to its circuit basics and how the oscillator works. Link here (PDF)
Today, the majority of electronic circuits (including microprocessors, microcontrollers, FPGAs, and cPLds) are based on clocked logic, requiring a timing source. depending on the frequency accuracy requirements, some employ oscillators while others use off-the-shelf quartz crystals in conjunction with the builtin oscillator circuit embedded in most microcontrollers and microprocessors.
Most if not all embedded solutions use the Pierce oscillator configuration, integrated as part of the Soc (systemon-chip). the obvious advantages include cost, size, and power compared to a standalone oscillator. the key limitation is the proper matching of the quartz crystal with the on-board Pierce oscillator.