Mount a Map or Poster Without Damaging It

If you want to use and reuse maps and posters without damaging them, you can use clear box tape and make it removable.

Steps

On each corner in the back, and in the center of the top edge (if it's heavy), put a couple of pieces of clear box tape, 5" long or so, next to each other, so that you've "laminated" a spot about the size of your open hand.
For each of those spots, cut a piece of box tape about a foot long. Make a loop of it, sticky side out, and overlap the ends. Wrapping it around your outstretched fingers is a good way.
Set one loop on each of the box-taped spots you've made on the back of the poster, and it will flatten down.
Stick it to the wall, pressing firmly where the tape is.
When you take it down, remove the loops and put them in the trash, and the corners will be clean and strong for the next time you want to put it up.

Use good box tape. Cheap tape won't hold things well and may leave a gummy residue behind.
Of course, you could just get the poster or map laminated, and use tape, but this way is cheaper and the map is easier to store between times if it's not fully laminated.
Use tacks but only put the sides of the tacks on it, not the point.
If your poster or map is too heavy for this method, you can do a similar thing on the front. Put tape on the front of the corners (all the way to the edge) and then tape it to the wall but put the tape over your "laminated" corner.
Use magnets. There are some strong magnetic poster hangers that hang posters without damaging them.

If the tape loop does get stuck to the paper, cut off whatever is not flat, and leave the rest, rather than try to peel it off and take part of the printing off too.