You will need:
Map
Glue Stick (does not need to be fancy)
Bangle Form (Use a bangle you already have to find something the same size. Mine is a coffee mug)
Decoupage medium (or liquid glue mixed with a bit of water)
Rotary Cutter (you can use scissors too, if you want)
Ruler
Board (to protect surface from blades
Memory wire
Scotch tape

*I got the idea for this from this instructable. I added a bit to make it more suitable for a larger size.

Step 1: Cutting the Paper

Using the rotary cutter, cut strips 3/4" wide. I ended up using thirteen 24" strips.

Step 2: Wrapping

Lay one of the strips down. This will be the inside of the bangle, so have a pretty/interesting side down.

Put a liberal amount of glue on the surface of the paper, making sure to get the edges.

Tape the end of the strip on the form, making sure the glue side is facing out.

Wrap the strips around the form, making sure the edges line up. When adding new strips, overlap the ends by a half inch or so.

Wrap a little less than half of your strips.

Step 3: Adding the Memory Wire

Halfway through wrapping, add memory wire. This gives the bangle more strength, making it less likely to get squished (as paper often is).

Cut a piece of memory wire that can wrap around the form and over overlaps about 3/4".

Put a piece of tape sticky side out on the wrapped strips. It should be higher than center.

Place the memory wire around the bangle, centering the overlapped ends over the tape. Make sure the wire is in the center of the strips the whole way around.

Fold the tape over the ends of the wire and press it together.

For the rest of the bangle, wrap strips glue side in. On the next strip, have extra glue and make sure you really press the edges down around the wire.

Let dry for a few hours.

Step 4: Finishing

Remove the bangle from the form and try it on. If it's too large, you can add more strips to the inside. This is a little trickier than wrapping them around, but it's not terrible.

Coat the bangle liberally in decoupage medium, being sure to coat the rough edges on the side. Let it dry on a rack, and move it every so often to keep it from sticking.

Add another coat or two until it seems very firm.

Step 5: Wear It!

Wear your beautiful bangle, and proudly tell everyone you made it yourself.

A really cool idea would be to make one out of a map from a certain trip, then get a charm that reminds you of the place you went and loop it through!