To find out who were the most constant players of the past years I took their year-end world rankings and calculated the standard deviation (which indicates the variation around the mean value). The higher the standard deviation, the more changes a player had in his year-end rankings.
The constancy is independent of the player's performance level, indicated by the mean value of his ranks in the corresponding period.

                       stddev      mean
Sampras, Pete            1.73      2.00
Krajicek, Richard        9.99     14.56
Rosset, Marc            15.44     30.11
Chang, Michael          15.94     13.78
Pioline, Cedric         17.78     30.22
Ferreira, Wayne         17.94     26.22
Ivanisevic, Goran       18.20     15.00
Fromberg, Richard       20.40     70.67
Tarango, Jeff           22.68     75.33
Clavet, Francisco       23.16     41.67