I have used cherry, maple, bamboo (not technically a wood, but whatever), padauk, wenge, zebrawood, leopardwood, katalox, chakte viga, black walnut, purpleheart, chechen, cedar, Bolivian rosewood and, oh something like olivewood, but not exactly sure. That last one was a butcher block style cutting board from Ikea. It was very stringy, and a pain to clean up the edges of the cuts. I still have a few of the cutting boards left. Not sure what I am going to do with them.
Anyway, my favorite looking wood is the Bolivian rosewood. The beautiful red-brown and black grain is so fantastic looking when polished up and oiled. I am a minimalist when it comes to my cribbage boards. I love the look of the grain of the wood, and I like to have the minimum amount of marking on the wood surface.
My favorite feeling wood is Katalox. This stuff is incredibly dense and fine grained. If you sand it to 400 grit and hit it with a coat of mineral oil, it will feel glossy - almost like it has a thin shellac on it. Did I mention it is dense? Also, as a side note, I do like the colors of it. A red-brown to dark brown heartwood, and a yellow sapwood. I still plan on making a checkerboard with the dark and light squares katalox.
I am lucky living near a port (Seattle) because there is so much inexpensive wood from around the world available to me, and I can stop and pick it up on my way home.
EDIT: For outdoor use, I cut some signs out of some Baltic birch plywood for my daughter. I used white spray paint to paint the surface and then v-carved them and then applied 3 coats of clear spray paint on them. I know, not too classy, and if I were not so lazy I would have picked a better outdoor wood, but it was a quick and dirty weekend job so she could get to selling chicken eggs, since her hens were laying like crazy and she had to start reducing her inventory. The sign has held up the last 18 or so months (at least one Washington winter) and still looks unaffected.