GLM FAQ
1. When do I demean (mean center) an EV?
If your EV is a covariate (of interest or not interest) then it is almost always advisable to demean this. Sometimes the results of particular contrasts do not depend on whether you demean or not (so not demeaning may not be "wrong" but it does not hurt). In other cases it is important to demean or the interpretability of the results is lost. If you have more than one group in your design then make sure you demean across all groups and not within each group.
For more on exactly what happens when you center and when it is or is not important, see Jeanette Mumford's guide on Mean centering continuous covariates for a group fMRI analysis.