The answer depends on the implementation, as is often the case when asking practical questions about quantum computing. To give you an example of the state of the art in trapped ions, the Lucas group in Oxford can achieve less than one error in 1 million single-qubit gates, which they claim is less than the fault-tolerance threshold. Their error rate for two-qubit gates is more like one in every hundred operations, which will not be sufficient for fault-tolerance. However, it seems likely that error rates for two-qubit gates will continue to decrease as technology develops.
The key issue in all of these implementations is scalability. It is not enough to demonstrate low error rates on just a few qubits. One also needs to be able to design an architecture allowing one to manipulate and store quantum information on tens or hundreds of qubits, while keeping the error rates low, before anything remotely useful can be done with your putative quantum computer.