Are there any dangers of hanging a bow vertical over a long period of time as opposed to hanging horizontal across two pegs?

Longbow or recurve?

Longbow, no.

Recurve, not if you are careful that the bow hangs straight down from the hook.  If your pegs (hooks) are too short, you can torque the bow against the wall and twist a limb.

Thanks Jeff. That was what I was looking for. I have both longbow and recurves and am needing to make room so, I wanted to hang them vertical to get more on one wall.

If you get a chance, check out the book "The Old Bowhunter".  Chet Stevenson had literally hundreds of bows in his study hung by a single peg.  I'd bet 70-80 percent of those were all wood bows to boot.

I think you should not hang them vertically for more than fifty years.  At least that has been my experience.  A little common sense goes a long way with such things.  An unstrung bow will not bend by hanging from a nail/peg.  Even a strung bow would have to be torqued on the peg to even make a slight difference.  I don't hang mine strung.