Catalyzes the covalent attachment of ubiquitin to other proteins. 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. S-ubiquitinyl-[E1 ubiquitin-activating enzyme]-L-cysteine + [acceptor protein]-N-terminal-amino acid = [E1 ubiquitin-activating enzyme]-L-cysteine + N-terminal-ubiquitinyl-[acceptor protein]. Protein modification; protein ubiquitination. Belongs to the ubiquitin-conjugating enzyme family.