A qubit is a quantum two-level system. Thus, in principle any pair of levels of any quantum system could be used as a qubit. However, there are many practical considerations, which result in a series of competing and complementary figures of merit, such as ease of operation, scalability or resilience towards noise.
In practice there are still many physical implementations that are being explored. This section on Wikipedia collects the most important ongoing attempts to physically implement qubits:.
For physically implementing a quantum computer, many different candidates are being pursued, among them (distinguished by the physical system used to realize the qubits):
Superconducting quantum computing (qubit implemented by the state of small superconducting circuits (Josephson junctions))
Trapped ion quantum computer (qubit implemented by the internal state of trapped ions)
Optical lattices (qubit implemented by internal states of neutral atoms trapped in an optical lattice)
Quantum dot computer, spin-based (e.g. the Loss-DiVincenzo quantum computer) (qubit given by the spin states of trapped electrons)
Quantum dot computer, spatial-based (qubit given by electron position in double quantum dot)
Nuclear magnetic resonance on molecules in solution (liquid-state NMR) (qubit provided by nuclear spins within the dissolved molecule)
Solid-state NMR Kane quantum computers (qubit realized by the nuclear spin state of phosphorus donors in silicon)
Electrons-on-helium quantum computers (qubit is the electron spin)
Cavity quantum electrodynamics (CQED) (qubit provided by the internal state of trapped atoms coupled to high-finesse cavities)
Molecular magnet (qubit given by spin states)
Fullerene-based ESR quantum computer (qubit based on the electronic spin of atoms or molecules encased in fullerenes)
Linear optical quantum computer (qubits realized by processing states of different modes of light through linear elements e.g. mirrors, beam splitters and phase shifters)
Diamond-based quantum computer (qubit realized by electronic or nuclear spin of nitrogen-vacancy centers in diamond)
Bose–Einstein condensate-based quantum computer
Transistor-based quantum computer – string quantum computers with entrainment of positive holes using an electrostatic trap
Rare-earth-metal-ion-doped inorganic crystal based quantum computers (qubit realized by the internal electronic state of dopants in optical fibers)
Metallic-like carbon nanospheres based quantum computers
The large number of candidates demonstrates that the topic, in spite of rapid progress, is still in its infancy. There is also a vast amount of flexibility.