Doc_M here is my take on the death of the conquistador. (spoilers head).

The beauty of this movie is that it allows for multiple interpretations of the entire time line and not just the ending.

One interpretation is that the movie is told using non-linear story telling. The non-linear interpretation leads to the following time line:
The protagonist loves his wife (in the year 2000). She dies while writing a book about Spain set in the 1500s. The protagonist's medical research leads to life extension technology. He prolongs his life for 500 years until the technology to travel through space becomes available. In a romantic gesture he casts his wife's remains (the tree) and himself into the nebula.

The second interpretation of the movie, which I feel more comfortable with, is that the scenes in the movie occur on a linear time line set in the year 2000 (i.e., There is no space travel). The scenes in the bubble are a visualization of the protagonist's inner space. We see this inner space every time the protagonist withdraws into himself. The scenes involving Spain are a visualization of the chapters in the book. They are shown every time someone writes into the book. In beginning the wife is doing the writing, and towards the end the protagonist is writing the final chapter as per his dead wife's wishes. The final scene shows the protagonist coming to terms his wife's death; the blooming tree is a visual depiction of his mind having an epiphany and the conquistador's death shows how the protagonist ended the book (accepting death as the spring of new life). Finally, once he has made peace with his wife's death he is able to fulfill her last wish - planting a tree over her grave.

Obviously Aronofsky wanted to make the movie consistent with the first interpretation. That is why the movie has the whole subplot involving the life-extending medical research. It is also the time line suggested by the movie's trailer. But I also think he consciously wanted the movie to be consistent with the second interpretation and this is not just me reading way too much into the story. The metaphor of 'mind as deep-space' is common in many mystic philosophies. You might have heard the term 'psychonaut' to describe people who engage in deep meditation or those who consume hallucinogens. Also, some of the scenes in the bubble show transitions of the protagonist withdrawing into his mind: example, consider the scene where he lies down with his wife on the hospital bed; the very next scene begins in the bubble and you can see the ghost image of the hospital bed and his wife slowly fading away as he is drawn into his mind.

For this and many others reason I love the Fountain.

In reply to this comment by Doc_M:
I think I've got this film figured out, but I still don't understand the death of the conquistador. If you get it, help me out here.