  Several new classes of compounds can be modeled in first approximation by
electrons on the triangular lattice that interact through on-site repulsion $U$
as well as nearest-neighbor repulsion $V$. This extended Hubbard model on a
triangular lattice has been studied mostly in the strong coupling limit for
only a few types of instabilities. Using the extended two-particle self
consistent approach (ETPSC), that is valid at weak to intermediate coupling, we
present an unbiased study of the density and interaction dependent crossover
diagram for spin and charge density wave instabilities of the normal state at
arbitrary wave vector. When $U$ dominates over $V$ and electron filling is
large, instabilities are chiefly in the spin sector and are controlled mostly
by Fermi surface properties. Increasing $V$ eventually leads to charge
instabilities. In the latter case, it is mostly the wave vector dependence of
the vertex that determines the wave vector of the instability rather than Fermi
surface properties. At small filling, non-trivial instabilities appear only
beyond the weak coupling limit. There again, charge density wave instabilities
are favored over a wide range of dopings by large $V$ at wave vectors
corresponding to $\sqrt(3) \times \sqrt(3)$ superlattice in real space.
Commensurate fillings do not play a special role for this instability.
Increasing $U$ leads to competition with ferromagnetism. At negative values of
$U$ or $V$, neglecting superconducting fluctuations, one finds that charge
instabilities are favored. In general, the crossover diagram presents a rich
variety of instabilities. We also show that thermal charge-density wave
fluctuations in the renormalized classical regime can open a pseudogap in the
single-particle spectral weight, just as spin or superconducting fluctuations.
