In real life people never burst into song at the sort of moments they tend to do so in the movies or theatre. This is a big shame. So you can rectify it in your games.

No, seriously.

If you foresee some particular encounters or situations that will probably occur in an upcoming session, you can prepare some suitable musical numbers in advance. You can even have accompanying music ready to go. Bonus points if the music is an original composition, but this is not really necessary, especially for those without the requisite talents.

Really. Have a significant NPC burst into song at some point in one of your future adventures. It could make for a truly memorable encounter.

Or it could reinforce the notion that the NPC is totally nuts.

Transcript

Obi-Wan: Given this convenient distraction, I Force Pull my laser sword from Grievous and start cutting down cyborgs.
[SFX]: Whooom!
Anakin: Likewise.
General Grievous: How tedious. Minions, the game is afoot!
[SFX]: Kzrzk
[SFX]: Kzrzk
GM: Grievous's guards attack with electro-quarterstaves.
Obi-Wan: I see they shop at the same bars we do.
[SFX]: Kzrzk
[SFX]: Whooom!
R2-D2: Quarterstaves?
R2-D2: Ho! Ha Ha! Guard! Turn! Parry! Dodge! Spin! Ha! Thrust!
[SFX]: Kzrzk
[SFX]: Whooom!
Anakin: What?
R2-D2: "Robin Hood Daffy", 1958. Only one of the best cartoons ever made.
Anakin: And what's the best?
[SFX]: Whooom!
General Grievous: {singing} Kill da Je-di!
General Grievous: {singing} Kill da Je-di!
R2-D2: Bingo.