The several RNA polymerases in eukaryotes each have their own means of termination. Pol I is stopped by TTF1 (yeast Nsi1), which recognizes a downstream DNA sequence; the endonuclease is XRN2 (yeast Rat1). Pol III is able to terminate on its on on a stretch of As on the template strand.
Finally, Pol II also have poly(A)-independent modes of termination, which is required when it transcribes snRNA and snoRNA genes in yeast. The yeast protein Nrd1 is responsible. Some human mechanism, possibly PCF11, seems to cause premature termination when pol II transcribes HIV genes.