RNA polymerase II transcribes both coding and noncoding genes, and termination of these different classes of transcripts is facilitated by different sets of termination factors. Pre-mRNAs are terminated through a process that is coupled to the cleavage/polyadenylation machinery, and noncoding RNAs in the yeast Saccharomyces cerevisiae are terminated through a pathway directed by the RNA-binding proteins Nrd1, Nab3, and the RNA helicase Sen1. We have used an in vivo cross-linking approach to map the binding sites of components of the yeast non-poly(A) termination pathway. We show here that Nrd1, Nab3, and Sen1 bind to a number of noncoding RNAs in an unexpected manner. Sen1 shows a preference for H/ACA over box C/D snoRNAs. Nrd1, which binds to snoRNA terminators, also binds to the upstream region of some snoRNA transcripts and to snoRNAs embedded in introns. We present results showing that several RNAs, including the telomerase RNA TLC1, require Nrd1 for proper processing. Binding of Nrd1 to transcripts from tRNA genes is another unexpected observation. We also observe RNA polymerase II binding to transcripts from RNA polymerase III genes, indicating a possible role for the Nrd1 pathway in surveillance of transcripts synthesized by the wrong polymerase. The binding targets of Nrd1 pathway components change in the absence of glucose, with Nrd1 and Nab3 showing a preference for binding to sites in the mature snoRNA and tRNAs. This suggests a novel role for Nrd1 and Nab3 in destruction of ncRNAs in response to nutrient limitation.