Octave-spanning optical frequency combs (OFCs) are essential for various applications, such as precision metrology and astrophysical spectrometer calibration. In this Letter, we demonstrate, for the first time to our knowledge, the generation of octave-spanning Kerr frequency combs ranging from 1150 to 2400 nm in aluminum nitride (AlN) microring resonators, by pumping the TM00 modes at 250 mW on-chip power. By simply adjusting the pump detuning, we observe the transition and coexistence of Kerr OFC and stimulated Raman scattering. For the TE00 mode in the same device, a broadband Raman-assisted frequency comb is demonstrated by adjusting the pump power and tuning. These results indicate a crucial development for the fundamentals of nonlinear dynamics and comb applications in AlN.