Advantages - Without them we'd be stuck up an unpleasant smelling creek without a paddle!
Disadvanages - You need to understand what the correlation is based upon and when it should (or more importantly should not) be applied.
Correlation between SPT and Cu after Stround 1974 is a good example. Graphs suggest Cu=SPT*4 to 5 (depending on PI), BUT, this data is based on results from overconsolidated clays so how much confidence should you have using it in other clays?
We need to use correlations because site investigation information is rarely comprehensive enough and ground conditions naturally vary - The majority of the pile and ground improvment design I do is based on empirical relationships. The key is to determine whether the soil parameter you're using is representative and try to understand how you're applying it.