The biggest example of a character contributing to the story, even after death was Dumbledore. He gave Harry the quest to find and destroy all of the horcruxes that were created by Voldemort. Harry had to keep faith in Dumbledore that he was correct and that Dumbledore knew what he was doing. Dumbledore's impact was felt way after his death in the form of Harry's quest and he was vital, maybe even more so than Harry in the downfall of Voldemort. He may have made some mistakes in his life, but he was devoted to stopping the dark arts and was a vital character, even in death. He even gives Harry some vital advice after he is dead and he got respect from most of the other characters.
Dumbledore isn't the only character that played a big role after death though. Surprisingly, Lily Potter, Harry's mom, played a huge role in this book. Lily is the reason that Snape was such a good character in this book. Without her influence and his continued love of her, Snape would never have been the hero that he was. If there weren't this tie between Lily and Snape, none of the plans that Dumbledore created would have worked and Voldemort would have stomped all over the wizardry world. Another key character after death was Dobby the house elf. Digging Dobby's grave is a key time for Harry. It helps him realize how foolish he was being by doubting Dumbledore and helped him get his head straight. The emotional shock of Dobby dying helped push Harry back into the right frame of mind which was key to the story.
When Harry and Hermione went to Godric's Hollow, Harry saw what was written on his parents tombstones which disgusted him. The tombstones said "the last enemy that shall be destroyed is death,". This reminded Harry of Voldemort's obsession of Mastering Death. I think he is not correct here and that he unfairly made this connection.
In Harry's parents case, mastering death meant that death was just the next step. The only way to truly defeat death is to not dread it or try to resurrect those who have been stolen by it, but is to continue to love those that have passed away, even if they aren't alive.
In Voldemort's case however, mastering death meant becoming immortal. He tried to achieve this by creating horcruxes and obtaining the Elder Wand (Deathstick, Wand of Destiny, etc.), one of the hollows. Death and Dumbledore were the only two things that Voldemort was afraid of.
Death is a very important topic to follow in this book.