Neither Raman nor IR Active vibrational modes
Yes it is possible. While no normal modes can be both IR and Raman active in molecules with a centre of symmetry, as mentioned in a comment molecules with silent modes exist. 

The easiest example is  probably the HCH out-of-plane twisting of ethylene: 

Source: http://www.shodor.org/succeed-1.0/compchem/labs/vibrations/ethylene.jpg

Due to the symmetry of the molecule, when the HCH twist out of plane the dipole and polarizability of molecule is unchanged.

Other examples can be found here

https://www.chem.purdue.edu/jmol/vibs/c6h6.html

where the modes of benzene are sketched. The silent modes easily seen are kind of distorted breathing of the ring, that due to the C6 axis of symmetry again let the molecule unchanged both for the electric dipole moment and its polarisability.