Is a Fetus a Person?

A comment made in one of Brandon’s posts posed the question, “is a fetus a person?” (I’ll make the assumption that a “person” is a human being with both spirit and body.) I believe so. Why? I think my belief spawns from the Bible. Take a look at Luke 1:41, 44:

41 And it came to pass, that, when Elisabeth heard the salutation of Mary, the babe leaped in her womb; and Elisabeth was filled with the Holy Ghost:
42 And she spake out with a loud voice, and said, Blessed art thou among women, and blessed is the fruit of thy womb.
43 And whence is this to me, that the mother of my Lord should come to me?
44 For, lo, as soon as the voice of thy salutation sounded in mine ears, the babe leaped in my womb for joy.

So it seems that John the Baptist, while still a fetus in his mother’s womb, lept upon hearing Mary’s salution? I think perhaps he may have felt the spirit of the Savior coming near.

Now that begs the question, when does the spirit enter the body, making the fetus a person? That I don’t know. I used to think conception, but now I tend to lean toward some time around the end of the first trimester. What are some of your thoughts?