Another vote for Vampires. Being a Malkavian is the highlight - for example, when the news announcer on the TV talks to you, it goes something like "Police today found a dead body in San Diego. They say they are looking for a suspect and they know it was you". Also, Jack's opening spiel in the tutorial made me realise straight away I was playing something special, Fat Larry's first lines cracked me up and some of the female characters are more proficient at flirting than any pixels have a right to be.

However, although it is monologue rather than dialogue, I would put in a word for the audio logs in System Shock 2. They tell a horror story so economically and vividly, finding the logs becomes more rewarding than the usual power-ups and goodies you root around for in RPGs.