Are there any good reasons to let a character die?

Solution 1:

There is a very specific benefit for killing off Wrex in the first game:

It is described in this answer.

The only way to Mordin alive is if Wrex is dead and you did not do Mordin's loyalty quest in ME2. You can then convince him to deliver the fake cure for the Genophage.

Another very minor point:

You have to kill off Morinth (if she counts as a party member) if you want Samara to be in ME3, as Morinth does not show up in ME3 at all.