Rose doesn't actually die, but gets transplanted to the parallel universe where she's to stay with Mickey, Jackie and the alternate universe version of her father. Although she gets to rejoin her family and friends, she loses the Doctor forever. The fissure between the two parallel universes is closed thanks to the efforts of the time traveling duo (and conveniently solves the matter of the invading Dalek and Cybermen forces by sucking them into the void), but in the process, Rose gets rescued by her alternate universe father and is transported to that version of Earth just as the fissures are closed for good. With no way to travel back and her body missing on our version of Earth, Rose Tyler is declared to be dead in our Earth.
This leads to the extremely moving final scene where the Doctor finds a way to communicate with Rose by burning up a star and projecting himself on a beach somewhere in Norway. Rose manages to track him down and find him, they have only a few minutes to speak, and before the Doctor can confess to a crying Rose that he loves her, the communications link is broken. It's extremely genuine and heartfelt and you really couldn't ask for a better way to say goodbye. Of course, life must go on, and as a tearful Doctor walks about the Tardis, a confused and angry woman in full wedding attire appears onboard to end the episode. This new storyline will continue in the forthcoming Christmas Special that will premiere on the BBC soon after you read this.
Billie Piper exits the show by setting the bar so high for the role of the Doctor's companion that one has to feel extremely sorry for Freema Agyeman. Rose Tyler's shoes are not going to be easy for anyone to fill. The comparisons are bound to happen and unlike Tennant replacing Eccleston at the beginning of this season, there are no real criticisms about Billie Piper's performance as Rose. She's been an extremely likable character that complements the Doctor extremely well.
While the denouement in this episode is clearly the emotional highlight, the main story is riveting and even on its own would have made for a geek's dream-come-true sci-fi epic. The Daleks and the Cybermen get to fight each other, and in the process exchange some extremely funny dialogue. A brief proposed alliance between the two robotic races is postulated by the Cybermen: "Together, we could upgrade the universe!" The Dalek leader dismisses the idea immediately and tells the Cybermen: "You are superior in only one respect… you are better at dying." It's quite witty and makes the episode that much more memorable.
For fans of the series, this is an extremely satisfying finale, and for those who have yet to witness this British cult phenomenon, if you're going to watch just one Doctor Who episode, "Doomsday" provides more entertainment than you would get in a full season of lesser shows. This is sci-fi television at its finest.