standard deviation

I've noticed that when calculating VaR/variance/std. dev of 2+ assets (or portfolio), sometimes the correlation/covariance is included, and sometimes it's not. I.e. for standard deviation of 2 assets: sqrt[w(1)^2*variance(1) + w(2)^2*variance(2)+2*w(1)*w(2)+covariance(1,2)] where (1) = asset 1...