Maybe I play a bit too much TF2, but I think it would help give the characters a lot more personality if they automatically taunted or said some line when they killed a person/building/etc, or in response to other events. I've still only played about half the champions, but I don't even know what the rest of them sound like (aside from their death screams). I might be more inclined to play a champion if I think they have an interesting voice or personality, as opposed to just blindly picking someone who looks cool.
I feel it would make the characters more interesting and add more variety to games. The only issue is probably the sheer amount of lines that would have to be added, but as it is I don't think we really hear enough out of our champions besides their general acknowledgment lines (Or anything at all in Rammus's case, I hope he gets a voice eventually). On that note, hotkeys for jokes, taunts, laughs, etc would be cool too!