Normally it is due to negative charged adsorbed chemical species/groups such corboxyl groups etc.

Depends on the pH and the stabilizers added to the system.  Often phosphate stabilizers are used and these are negatively charged (PO42-).  Biomolecules are almost invariably negatively charged at neutral pH (~ 7). 

Proteins are often used as capping agents, adsorbing on NP surface and stabilizing dispersions by means of steric effects. In such cases the resulting  z-potential is usually negative, yet low in absolute value (>-30 mV). I guess if you use BSA or other proteins to stabilize your metallic NP dispersions you might end up with a well stabilized suspension with a moderate negative surface charge.

@ Vinod I'm not sure where you get your statement that "As we are knowing Ag/Au nanoparticles don't have any charge".  In air this is certainly not the case.  ESCA/XPS and Auger will show that the surfaces (top 5 - 10 atomic layers) are in the fully oxidized state - Ag+ and Au3+ plus up to around 30% C (used to calibrate for the oxidation state at 285 ev).  It's the surfaces of course that interact with the environment.  Only in a reducing environment or freshly cleaved surfaces in vacuum will produce neutrality.  Argon ion milling is often used to remove these top 5 or 10 layers to reveal the bulk composition.  Chemisorption induced segregation is the mechanism in air pulling species to the surface.  Another example of this is in froth flotation where freshly cleaved galena (PbS) won't float with xanthate collectors.  Bubbling air through with a sparger oxidizes the surface and this produces Pb2+ which can be floated with the S2- charges on the xanthate.  See (for example):

Nov 11th, 2008. Dispersion and nanotechnology

http://tinyurl.com/hpywsge

On another theme Ag0 is not soluble in water whereas Ag+ is (and is the effective bactericide).  See:

September 2nd, 2015 Silver colloids and invisible ink

https://www.brainshark.com/malvern/vu?pi=560497681&b=1&tx=120486&c1=22

Normally when your medium is alkaline you may get negative zeta potential. In general positive or negative value of the zeta potential depends on the pH of the media. Higher zeta potential will impart stability to nanoparticles in suspension due to repulsion among the particles whereas low zeta potential leads to coagulation.

It´s quite normal that metals acquire surface charges when added in aquous media due to the polar caracter of water molecules  (see double layer/stern layer). This charge will result in a eletric potential.

The zeta potential will depend on pH and, as prevoiusly said by Dr. Tarafdar, and alson on the electrolyte concentration.