The key problem is not correlation but colinearity. Correlation is neither a necessary nor a sufficient condition for colinearity. Condition indexes over 10 (as some authors say) indicate moderate collinearity, over 30 severe, but it also depends on which variables are involved in the collinearity.
If you do find high colinearity, it means that your parameter estimates are unstable. That is, small changes in your data can cause big changes in your parameter estimates (sometimes even reversing their sign). This is a bad thing.
Remedies are 1) Getting more data 2) Dropping one variable 3) Combining the variables (e.g. with partial least squares) and 4) Performing ridge regression, which gives biased results but reduces the variance on the estimates.
So you have some solutions. Hope it helps