Theoretically, any superposition can be experimentally realized. Experimentally, most can't. The fundamental reason is that a system must be decoupled from its environment so as not to decohere, yet still coupled strongly to an extremely well-calibrated apparatus to generate the superposition. I would guess the 'advanced information' for the 2012 Nobel Prize would be a good starting point, since this issue was so central for both Haroche and Wineland.
SuperpositionsAs a very rough experimental summary, superpositions of two-level systems has been seen in a huge number of systems, from charge or flux states in qubits to magnetic or electronic states in atomsof semiconductor impurities. A general superpositions on the order of up to maybe half a dozen states has been realized in a few systems, namely. The systems that leap to mind are nuclear spins in a molecule, internal spins in an atom, the spin/electronic state of a chain of ions, momentum state of a free-falling aotm, or the polarization and spatial mode of one (or several) photons. For instance, superpositions such as $a|0\rangle + b |2\rangle$ can be made with photons, where $|n\rangle$ is the photon numbers.
For a large number of particles, very particular superpositions can be made. For example, spin squeezing has been observed for probably hunderds to thousands of atoms, but a general superposition state of so many atoms is beyond current experiments. That, in a word, is why it's hard to build a quantum computer.
To answer the broader question, superpositions are very useful to know about and understand, even if they're very challenging to make.