The results of simultaneous observations of oscillations in the chromosphere, transition region, and corona above nine sunspots are presented. The data are obtained through coordinated observing with the Solar and Heliospheric Observatory — SOHO and the Transition Region And Coronal Explorer — TRACE. Oscillations are detected above each umbra. The power spectra show one dominant frequency corresponding to a period close to 3 min. We show that the oscillations in the sunspot transition region can be modeled by upwardly propagating acoustic waves. In the corona the oscillations are limited to small regions that often coincide with the endpoints of sunspot coronal loops. Spectral observations show that oscillations in the corona contribute to the observed oscillations in the TRACE 171 Å channel observations. We show that a recent suggestion regarding a connection between sunspot plumes and 3-min oscillations conflicts with the observations.