I have seen people who wrap the Tefilin 7 times around their arm and some that wrap it 8 times around their arm. Why do the people who wrap it 8 times do so?
The part of the arm that matters when counting the number of loops around the arm is from the elbow to the wrist. The Chabad custom is to wrap the straps so that there are 6 complete loops and 2 half loops. This equals 7 complete loops, but may look like one is wrapping 8 loops.
As you can see from this picture from Chabad.org's article about Tefillin, the view of the inner arm and outer arm both have 7 loops between the wrist and the elbow. However, the view of the inner arm is 2 loops, a space, and then 5 loops, while the view of the outer arm is 3 loops, a space, and then 4 loops.
This is because the first and last loops are only 1/2 way on the arm (between the elbow and the wrist), and are only visible on one side (of that part of the arm), respectively.
I wrap it seven times, but have been told I wrap it eight times because people count differently than I. That is, from the elbow, I wrap it half a time, seven full times, and whatever's necessary to bring it around again (i.e., another half). So it's seven, see? No, really. Seven. Count 'em.
No, count 'em this way.
As to why I put the extra halves, I don't know, except that my father does (and, presumably, his father did, and his father, etc.).
I don't know about 8 times, but the Shulchan Aruch OC 27:8 says
ונוהגין העולם לכרוך על הזרוע ששה או שבעה כריכות
The custom is to wrap [the strap] around the forearm 6 or 7 times.
It seems not only that we should be discussing 6 or 7 and not 8, but also that the exact number doesn't really matter.
Can't remember the source, but I remember seeing somewhere to wrap 8 times around the arm. Be'ezrat HaShem Beli Neder source coming soon.
As Msh210 wrote up there it is really 7 with an extra half (see Siah Yitzhak Siman 5): ועל הזרוע שמונה כריכות, כי כריכה ראשונה אינה במילואה ואינה נחשבת
The first one doesn't count because it is incomplete.
In addition to the Minhagim mentioned, it also is closely related to the direction one wraps. Wrapping inward tends to make it obvious how many loops there are, whereas wrapping outward leaves it unclear, hence the need for different Minhagim (6 and 2 halves, 7 and a half, etc.) to make an extra loop to ensure 7 complete loops.