Electronic excitations in AlxGa1-xAs-GaAs quantum wires and quantum dots have been investigated by means of resonant inelastic light scattering. At low frequencies, we find quasi-one-dimensional and quasi-zero-dimensional confined plasmons. Interestingly, we observe, at higher frequencies, not only the original two-dimensional (2D) intersubband excitations, but additional modes ωk in polarized scattering geometry. The experimental finding is that the frequencies of these modes obey the relation ωk2≊ω2D2+ω 1D/0D2, where ω2D is the frequency of the vertical intersubband charge-density excitation. ω1D is a lateral quasi-one-dimensional confined plasmon frequency in wires and ω0D is the frequency of a quasi-zero-dimensional confined plasmon in dots. This relation shows that the additional modes are collective charge-density excitations, which occur due to a coupling of lateral and vertical electron motion.