The effect of the band structure anisotropy (triangular, square, and hexagonal wrapping) on the electronic collective excitations (plasmons) in a two-dimensional electron gas (2DEG) is studied in the framework of the random-phase approximation. We show that the dynamical dielectric response in these systems strongly depends on the direction of the in-plane momentum transfer q. The effect is so pronounced that it results in a different number of electronic collective excitations in some q regions, both with - and ∼q-like energy dispersions. This finding is in striking contrast to the conventional 2DEG case with isotropic energy band dispersion where only a single plasmon with dispersion can exist. Our prediction of acoustic modes (with the ∼q dispersion) in a one-energy-band electron system expands the previous knowledge that such kind of plasmon can be realized only in two-component systems.