This is an interesting question for me because I really don't consider myself an expert in this subject. I'll run down a few though, then if I miss one you're interested in, just let me know and I'll say a bit about that one too.
First - wood dust is a carcinogen, all wood dust. Some are an even bigger PITA, and are toxic, and some will actually cause you to be allergic to wood. Always wear a respirator.
Desert Ironwood. Who doesn't like the look of desert ironwood. It boasts the best chatoyance of any wood I've worked with. Chatoyance is the property of wood that makes it look deep, and kinda changes in the light when you shift its position. But its a super PITA to work. Stinks like hell, burns easy, and gums up files and sandpaper worse than any other wood I work. Oily woodes gum up files, and its the high oil content that make them naturally stable. Unfortunately, its also kinda endangered, and won't be available for long.
Osage. I love working this wood. Its hard as snot, and stable enough without gumming up files too bad. It burns easy though, so you have to use sharp belts.
Paduk. Lots of chatoyance here too. And sometimes you can find this gorgeous blond streak running through the dark pinkish color. Really toxic.
African Blackwood. This is my ebony substitute. Ebony is gorgeous, but cracks and checks like a bear. Blackwood is more stable, and greasy. Expensive stuff. Smells good when you work it. Finishes up just as good as ebony.
Cocobolo - Man I love this stuff, but its super toxic. The dust will irritate the skin, the lungs, the eyes. Its a sensitizer, which means it will cause wood allergies. I wear long sleeves taped to my arm, pants, gloves, full face mask, etc when I work it. That said, its stable and gorgeous. Sometimes it seems you can find every color in the rainbow in there. Lots of chattoyance.
Bocote. Man, God designed an ideal knife handle wood in this one. Gorgeous, hard, stable. Never seen a piece I didn't like.
Masur Birch - This is a N. European Birch, and has really beautiful figure throughout. A little soft, but stable. I love it when I can get it.
Maple - red. I like using maple. Its an American staple. Some guys have every piece stabalized, but I usually don't. I get the curly stuff cheap at a spot near my home because cabinetmakers think of curly wood as trash...
Wenge - I've recently fell hard for Wenge. Its hard, and greasy. IMO, it just looks passionate. There is so much going on in there. Its fiery looking.
East Indian Rosewood. This is the very dark brown Rosewood that i use a lot. This is again because I get it nice and cheap. Greasy and hard, stinks when you work it. Just gorgeous when you finish it.
Hickory. I got 11 board feet of curly Hickory for $22 last year. I've made two knives from it and I'm impressed. Its damn hard though.
For finishes, I like two basic methods. Plain oil, I usually choose Danish oil. Dip whole handle, allow to dry for 10 minutes, wipe. Repeat next day. Wax next day. Or a polyurethane dip. I dip the whole handle and allow it to soak for ~15 minutes. Then I drain it and wipe it all the way off. Next day I rub it down with scotchbrite, and re dip.
I don't stain my woods very often. I guess I should stain my curly maple more, but I really like the wood natural. There is every color and texture imaginable, so I leave the wood as is. Over time, the sun will darken the woods, and bring that curl out anyway.
Any specifics I missed?