Direction of Arrival (DOA) estimation is a fundamental problem in acoustic signal processing. It is used in a diverse range of applications, including spatial filtering, speech dereverberation, source separation and diarization. Intensity vector-based DOA estimation is attractive, especially for spherical sensor arrays, because it is computationally efficient. Two such methods are presented which operate on a spherical harmonic decomposition of a sound field observed using a spherical microphone array. The first uses Pseudo-Intensity Vectors (PIVs) and works well in acoustic environments where only one sound source is active at any time. The second uses Subspace Pseudo-Intensity Vectors (SSPIVs) and is targeted at environments where multiple simultaneous sources and significant levels of reverberation make the problem more challenging. Analytical models are used to quantify the effects of an interfering source, diffuse noise and sensor noise on PIVs and SSPIVs. The accuracy of DOA estimation using PIVs and SSPIVs is compared against the state-of-the-art in simulations including realistic reverberation and noise for single and multiple, stationary and moving sources. Finally, robust performance of the proposed methods is demonstrated using speech recordings in real acoustic environments.