Catalyzes the covalent attachment of ubiquitin to other proteins. Plays a role in transcription regulation by catalyzing the monoubiquitination of histone H2B to form H2BK123ub1. H2BK123ub1 gives a specific tag for epigenetic transcriptional activation and is also a prerequisite for H3K4me and H3K79me formation. Also involved in postreplication repair of UV-damaged DNA, in N-end rule-dependent protein degradation and in sporulation. S-ubiquitinyl-[E1 ubiquitin-activating enzyme]-L-cysteine + [E2 ubiquitin-conjugating enzyme]-L-cysteine = [E1 ubiquitin-activating enzyme]-L-cysteine + S-ubiquitinyl-[E2 ubiquitin-conjugating enzyme]-L-cysteine. Protein modification; protein ubiquitination. Belongs to the ubiquitin-conjugating enzyme family.