If you set paramagnetic structures aside, there are up to +2/-4 ppm variations in the chemical shifts of aromatic residues (Phe, Tyr, Trp) from the average values. Variation in non-aromatic residues is not smaller, so it probably has more to do with the local environment rather than the nature of the residue itself.
The chemical shift variation is far greater (may be hundreds of ppm) in paramagnetic species due to contact and pseudocontact shifts.
BMRB - Biological Magnetic Resonance Data Bank has the most comprehensive collection of such data, including histograms of chemical shifts in each aminoacid. Their "outlier" tables list chemical shifts of each atom and give link to the source data.
The chemical shift variation is far greater in paramagnetic species due to contact and pseudocontact shifts.
This page has links to histograms assembled from full set of protein data and this one has data from diamagnetic proteins only.
This paper (by Nian E. Zhou, Bing Yan Zhu, Brian D. Sykes and Robert S. Hodges) has a discussion of amide chemical shift in relation to the length of the hydrogen bond on an amphipathic alpha-helical peptide which has a curved geometry (bent towards the hydrophobic part). Amide chemical shift changed by a maximum of +/- 0.7 ppm compared to the random coil value, where increase corresponded to the hydrophobic lobe and decrease - to hydrophilic lobe, so the shorter is the hydrogen bond, the higher is chemical shift of the amide residue.