So, here's what I had to do: I used fishing line and goo-gone fished behind the emblem. I sawed it back and forth slowly working across the emblem.

Things to look out for (learn from my mistakes):
1. If you don't pull the fishing line away from the car, you'll wind up scoring the plastic on the rim of the indention.
2. The four knobs under the emblem are for the alignment, and they make running the fishing line completely across, so I separated the top and bottom, then used a flat tip screwdriver with a small piece of rubber to prevent marring the paint and pried it the rest of the way off.
3. Even using paper towels to clean the spray of the goo-gone (I made the mistake of buying the spraybottle) will scratch the paint. I eventually came to the conclusion that soap and water and a microfiber cloth are the best way to clean overspray.
4. Most people recommend using dental floss for badge removal, which was fine for removing the "370z", but the edges of the hamburger are sharp, and it's difficult to get it behind the badge, so in my experience, it was too thin and continuously broke.

Go forth and good luck.

This is why you use a Bondo spreader.:tiphat:

I realize this thread is old, but figured I would share my method of removing the emblem. The front emblem was fairly easy to get off with heat and dental floss, but the rear emblem gave me some troubles. So here's what I did.

Step 1:
Drill a hole at each end of the emblem. I was careful not to drill into the bumber, only through the surface of the emblem. The holes are needed to help pull the emblem off of the car. I actually only needed one hole.
https://farm9.staticflickr.com/8747/...5ea668_z_d.jpg

Step 2:
Heat up the emblem with a hair dryer.

Step 3:
Use a metal rod to pull, not pry, the emblem away from the car. I just hooked it into one of the holes and pulled away from the car. It came off really easy.
https://farm8.staticflickr.com/7637/...cd9bd9_z_d.jpg

Step 4:
Use a grinding tool to remove the two nipples that held the OEM badge. I covered the surrounding area with painters tape protect it.
https://farm8.staticflickr.com/7284/...3e1e29_z_d.jpg

https://farm8.staticflickr.com/7609/...68985b_z_d.jpg

https://farm8.staticflickr.com/7628/...fb7da5_z_d.jpg

Step 5:
Clean up the area and apply the new emblem

And here are the results
https://farm8.staticflickr.com/7606/...5eebee_z_d.jpg

https://farm9.staticflickr.com/8739/...3665d7_z_d.jpg