Ubiquitin-dependent proteolysis is catalyzed by the 26S proteasome, a dynamic complex of 32 different proteins whose mode of assembly and mechanism of action are poorly understood, in part due to the difficulties encountered in purifying the intact complex. Here we describe a one-step affinity method for purifying intact 26S proteasomes, 19S regulatory caps, and 20S core particles from budding yeast cells. Affinity-purified 26S proteasomes hydrolyze both model peptides and the ubiquitinated Cdk inhibitor Sic1. Affinity purifications performed in the absence of ATP or presence of the poorly hydrolyzable analog ATP-γ-S unexpectedly revealed that a large number of proteins, including subunits of the skp1-cullin-F-box protein ligase (SCF) and anaphase-promoting complex (APC) ubiquitin ligases, copurify with the 19S cap. To identify these proteasome-interacting proteins, we used a recently developed method that enables the direct analysis of the composition of large protein complexes (DALPC) by mass spectrometry. Using DALPC, we identified more than 24 putative proteasome-interacting proteins, including Ylr421c (Daq1), which we demonstrate to be a new subunit of the budding yeast 19S cap, and Ygr232w (Nas6), which is homologous to a subunit of the mammalian 19S cap (PA700 complex). Additional PIPs include the heat shock proteins Hsp70 and Hsp82, the deubiquitinating enzyme Ubp6, and proteins involved in transcriptional control, mitosis, tubulin assembly, RNA metabolism, and signal transduction. Our data demonstrate that nucleotide hydrolysis modulates the association of many proteins with the 26S proteasome, and validate DALPC as a powerful tool for rapidly identifying stoichiometric and substoichiometric components of large protein assemblies.