In bacteria, termination of RNA transcription can be rho-dependent or rho-independent. The former relies on the rho factor, which destabilizes the DNA-RNA heteroduplex and causes RNA release. The latter, also known as intrinsic termination, relies on a palindromic region of DNA. Transcribing the region causes the formation of a "hairpin" structure from the RNA transcription looping and binding upon itself.  This hairpin structure is often rich in G-C base-pairs, making it more stable than the DNA-RNA hybrid itself.  As a result, the 8 bp DNA-RNA hybrid in the transcription complex shifts to a 4 bp hybrid.  These last 4 base pairs are weak A-U base pairs, and the entire RNA transcript will fall off the DNA.
Transcription termination in eukaryotes is less well understood than in bacteria, but involves cleavage of the new transcript followed by template-independent addition of adenines at its new 3′ end, in a process called polyadenylation.