Theory and some evidence support classical signaling and computation in microtubules and other cytoskeletal components. These are thought to occur due to coherent Frohlich excitations, cellular automata activities, and/or ferroelectric and spin glass behavior in microtubules and associated water. Verification of such a proposed communication system---microtubules as classical computers--- would be a major breakthrough in cell biology. It is argued here, however, that even such an astounding discovery would not be the complete story. Through theoretical investigation of the nature of consciousness the conclusion has been reached that while microtubules may be classical computers, they are also capable of quantum computing. Present-day and near-future classical computers now appear to be an intermediate step in the evolution of computation toward quantum computers, an original suggestion of Benioff and Feynman in the 1980's. The idea (refined by e.g. Deutsch, Josza, Lloyd and others) is that quantum coherence can implement multiple computations simultaneously, in parallel, according to quantum linear superposition. Information is superposed and computes in the form of "qubits" in a quantum state which then is caused to "collapse" (quantum state reduction) to definite "bits", or particular results. Mathematical analysis has shown that quantum computers would be vastly superior to classical computers in important application areas. The current aim of a large volume of intense research, quantum computers may or may not ever be technologically feasible. Nonetheless it is now clear that quantum computation is in principle possible, and at least in some respects orders of magnitude superior to classical computing. The search for a mechanism of consciousness (in particular the problems of conscious experience, integrated binding, non-computability, and free will, transition from pre-conscious processing to consciousness) has led a number of theorists to propose macroscopic quantum states in the brain. The Penrose-Hameroff model suggests that quantum superposition and Penrose's objective reduction ("OR") occur in microtubules in groups of brain neurons and glia interconnected by gap junctions. The proposed microtubule quantum states and cycles of self-collapse are proposed to be bioenergetically pumped (e.g. Frohlich mechanism), isolated by cycles of actin gelation,orchestrated by microtubule-associated proteins, and coupled to neural-level activity (e.g. coherent 40 Hz). It is further suggested that quantum coherent superposition of microtubule subunits enables quantum computation which correlates with pre-conscious processing. The quantum superposition/computation (qubits) continues only until the Penrose quantum gravity threshold for self-collapse is reached. At that instant orchestrated objective reduction ("Orch OR" - self- collapse) occurs. We suggest each Orch OR event is conscious because (following a "pan-experiential" philosophical view along the lines of Leibniz, Whitehead, and Wheeler) each event accesses and rearranges "funda-mental" experience embedded in Planck scale spacetime geometry. The events also choose (non-computably) microtubule states (qubits -> bits) which regulate neural activity. A sequence of events (e.g. at 40 Hz) can give rise to a "stream" of consciousness. Consciousness may involve neurobiological processes extending downward within neurons to the level of the cytoskeleton, and accessing fundamental experience at the most basic level of reality. This conclusion rests on a premise that, as a precursor/substrate for consciousness, eukaryotic living systems in general must utilize quantum coherent superposition in microtubules. (The difference between a conscious and non-conscious living system being that, in conscious states, the quantum superposition self-collapses due to the Penrose objective reduction whereas in non-conscious states the quantum superposition is collapsed by environmental decoherence---as would be the case in proposed technological quantum computers.) Microtubules are structurally suitable for computation. Can they assume quantum coherent superposition? Evidence and theoretical considerations for quantum states in individual proteins and specifically in microtubules will be discussed.