Even though the word "death" never shows up in this poem, "Remember" is definitely a "death" poem if there ever was one. It might as well have been called "Remember me… after I'm good and dead," because that's the basic idea, concern, and preoccupation of Rossetti's sonnet. The speaker does her best to suggest that death is totally permanent—no more touching, talking, or any of that. In the end, this poem isn't really about that, but rather about different ways in which death isn't always the end.
In the end, death really can't win. Those "vestiges" the speaker describes are an example of how life finds a way to cheat death. (Face, death. Face.)
Pack your bags, gang. Death is nothing more than a journey to a new land, a transition from one place to another.
If "Remember" is a "death" poem, it is just as much the opposite as well: a "life" poem. Remember that part in Jurassic Park where Malcolm says "life… finds a way"? Yeah, that could be totally be this poem's motto, and it is through the memory that life finds a way. It is through memory that things live on, even after they're dead and gone. The other side of the coin, however, is that that remembrance can be, well, really painful. If we have fond memories of somebody who has died, we can't remember them without also facing the fact that they are no longer with us.
Memory is so awesomely powerful that it can cheat death. The cost of that cheating, however, is intense pain; if the speaker's beloved keeps her alive in memory, after all, he will also be very sad.
Meh—sometimes it's just easier to let the past be the past, and move forward with our lives. This is the lesson the speaker learns, and accepts, by the end of the poem.
Romeo and Juliet this poem is not, but love is definitely in the air. Hand-holding, plans for the future, turning back for one last glance—yep, that sure sounds like love to us. "Remember" is definitely a poem spoken by one lover to another, and it's sort like a here's-what-I-want-you-to-do-if-I-die type thing. The speaker dearly loves the guy she addresses, so much so that, even though she wants him to remember her, she doesn't want him to suffer. This is why, at the end, she would rather he forget her, than remember her and be sad.
Love really is a kind of possession (but not necessarily of the demonic kind). Look at all the hand holding and the speaker's inability to "turn" away, for example.
True love is about sacrifice more than anything (even cutsie nicknames). The speaker of "Remember" proves her love by saying she would rather her lover be happy than remember her.