Can metals have a net negative charge
These species usually do not exist in nature, but they can be synthesized.


Silver has been reduced in liquid ammonia to give $\ce{Ag-}$.
A lot of anionic metal carbonyl complexes $\ce{M(CO)_{n}^{m-}}$ have been synthesized: 


-1


$\ce{[V(CO)6]-}$, $\ce{[Nb(CO)6]-}$, $\ce{[Ta(CO)6]-}$, $\ce{[Mn(CO)5]-}$, $\ce{[Ir(CO)4]-}$, $\ce{[Co(CO)4]-}$, $\ce{[Rh(CO)4]-}$


-2


$\ce{[Ti(CO)6]^{2-}}$, $\ce{[Zr(CO)6]^{2-}}$, $\ce{[Hf(CO)6]^{2-}}$, $\ce{[Fe(CO)4]^{2-}}$, $\ce{[Ru(CO)4]^{2-}}$, $\ce{[Os(CO)4]^{2-}}$


-3


$\ce{[V(CO)5]^{3-}}$, $\ce{[Nb(CO)5]^{3-}}$, $\ce{[Ta(CO)5]^{3-}}$, $\ce{[Mn(CO)4]^{3-}}$, $\ce{[Re(CO)4]^{3-}}$


-4


$\ce{[Cr(CO)4]^{4-}}$, $\ce{[Mo(CO)4]^{4-}}$


There's a review by John E. Ellis: Highly Reduced Metal Carbonyl Anions: Synthesis, Characteri's zation, and Chemical Properties on these compounds.


Edit

While Christian Aichinger's comment concerning $\pi$-backbonding in metal carbonyls is correct, it is important to realize that $\ce{CO}$ is a neutral ligand! 

With other words: The Mond process: $\ce{Ni(s) + 4CO -&gt; Ni(CO)4}$, using nickel powder and carbon monoxide, is not a redox reaction and the oxidation state of the metal still is $0$ in the metal carbonyl.