Highly accurate and precise crystal structures of methyl alpha-D-arabinofuranoside, methyl beta-D-ribofuranosidc, methyl alpha-D-lyxofuranoside, and methyl alpha-D-xylofuranoside have been determined at 100 K by X-ray crystallography. The structures of methyl alpha-D-arabinofuranoside and methyl beta-D-ribofuranoside have also been determined at 15 K by neutron diffraction. Equilibrium (r(e)) geometries of the same compounds were computed by means of density functional methods using a variety of exchange-correlation functionals and a sequence of basis sets. The validity of the computed results was assessed by several criteria including agreement between computed and observed bond distances and bond angles, agreement between computed and observed ring conformations, and basis set convergence of the computed geometrical parameters. Particular reference was made to computed internal hydrogen bond parameters, which are especially sensitive to the quality of the theoretical treatment. Because of the intrinsic sensitivity of the conformation of the five-membered ring to bond lengths and bond angles, molecular mechanics and small basis set SCF treatments are wholly inadequate. Local density functional theory also fails because of a tendency to strongly underestimate internal hydrogen bond distances. When the B3LYP exchange-correlation functional is used, bond lengths and bond angles agree with the neutron diffraction values to within their experimental uncertainty and the ring conformation is qualitatively correct, as long as a basis set of at least double-zeta plus polarization quality (such as cc-pVDZ) is used. Further expansion of the basis set leads to more accurate equilibrium bond lengths: and bond angles but does not appreciably affect the ring conformation. For methyl alpha-D-arabinofuranoside, methyl beta-D-ribofuranoside, and methyl alpha-D-xylofuranoside, there is very good correspondence between the best computed and observed ring conformations, even though some intermolecular hydrogen bonds in the crystal give way to internal hydrogen bonds in the predicted gas-phase structures. On the other hand, in the case of methyl alpha-D-lyxofuranoside, an O2H ... O4 internal hydrogen bond between the ring oxygen O4 and the hydroxyl hydrogen of a ring carbon (O2H) in the computed structure leads to a very large change of ring conformation from the northeast corner of the pseudorotation pathway (P = 28 degrees, crystal) to the southeast corner (P = 130 degrees, computed).