Answer:
Probably the most common is 'make love' when you mean 'have sex'; another common euphemism on the same subject is 'I love ...', when you mean, 'I desire...', 'I need...", 'I want...'. In people's mind, these last three mean the same thing, but therein lies so much of relationship problems and where people are hurt the most. People don't know they're not thinking about it clearly, but such is 'love (hormones)'.
The next most common use of euphemisms is for someones' death; 'he passed away', 'she's left us', 'he's gone', or 'she's at rest'. When people use these euphemisms, they're not trying to fool anyone, they're just trying to be more gentle emotionally.