  We consider a weakly interacting massive particle (WIMP) dark matter (DM)
annihilating into all possible Standard Model (SM) particle pairs, including
the SM neutrinos, via $s$-wave processes and derive the branching ratio
independent upper limit on the total annihilation cross-section $\langle \sigma
v \rangle$ using the data of CMB, gamma-ray, cosmic-ray and several neutrino
observations. For conservative choices of all relevant astrophysical
parameters, we obtain upper limits of $10^{-23}-10^{-25}\,{\rm cm}^3{\rm
s}^{-1}$ on the total $\langle \sigma v \rangle$ for the WIMP mass range
$10\,{\rm MeV}-100\,{\rm TeV}$, thus making the entire mass range consistent
with the observed relic density. An important input that goes into our analysis
is the assumption that thermal WIMPs can have significant coupling to the SM
neutrinos.
