FYI: I originally created the map a few years back, so for the purposes of this instructable, I'm creating a smaller example for the step by step instructions.
Step 1: Gather Supplies
map (It's important that the map be a detail of a city so that the streets are large enough for you to cut around. My large map was a tourist map from a hotel that I got when traveling. The example in the following steps was printed from an online map.)
paper larger than map (I originally chose to use plain white paper for a minimalist effect, but since my second map is much smaller, I decided to use a magazine image from a large fashion magazine. I would have loved to use an image of the town in the map. Perhaps someone else would like to go that route.)
Step 2: Placement
If there's an image on the front, use a window to see through the papers and make sure it's placed the way you want.
I used masking tape, but just about any type that will cut easily with an x-acto would work.
Step 3: Cutting
Tip: Cut all the vertical lines and then all the horizontal. This will save you time by not having to rotate the map all the time and help you to cut straight.
Tip: If you aren't confident in your ability to cut a straight line, lay a ruler next to each line you need to cut as a guide. A clear ruler is best to avoid a wrong cut.
Tip: When cutting the horizontal lines that complete the cutting out of a section, start from the middle and work your way out. This will help the tape hold the map in place for longer.
Trim the edges.
Step 4: Display
Tack it directly to the wall
Frame it with a colorful piece of paper behind it
Frame it with nothing behind it. (The trick to this is to have extra room around where the map is cut out. Cut cardboard and tape it to the frame around the edges. I also nailed a couple scrap pieces of wood to the frame to get it further away from the wall.)
To Laser or Not to Laser?
While I completely agree with those stating in the comments below that cutting paper with a laser is just cheating, how cool would it be to cut a similar project from wood or some other material that would make you cringe at the thought of cutting it by hand. A strong wooden one could be made into a nice sturdy lamp to project your travels onto your bedroom wall while you dream of the location of your next exotic adventure.