Here's the following death I could remember:
Wishing well (Romantic Garden)
Death by Pufferfish (City Living)
Overheating/steamy? (Spa Day/Seasons)
Rodent Fever (My First Pet Stuff)
Rocket Fail... I don't know what it's called, but sims can die when they're failed to try to go to space
As for killing them by embarrassment or anger, you could set them up a scene. Make them wet their pants, walk in someone's privacy or being rejected when proposing (I haven't tried it but I've seen simmers here doing the same method)
And one of my sims died of anger after arguing with his enemy and caught his wife cheating on him. It's pretty easy :p
But if you don't mind cheating, there's a cheat to reach those specific emotions, but I don't remember...