I made a bow from dogwood years ago. It was okay. Hard to say if it just being okay was due to the wood itself, or my relative lack of experience back then.
I've made a few bows of elm. Sometimes this wood is great, sometimes not. There was a thread on this recently started by Marc St Louis. Like him, I haven't learned to tell a good elm from a bad elm before I invest the time turning the wood into a bow. I don't like that, so don't gravitate towards elm very often.
As for hickory, I think other folks have characterized it well. Of the white woods, the only one I'll choose above hickory is eastern hophornbeam. Hickory is relatively easy to find as a nice straight stave, easy to split, and very tough. It takes tempering very well, and especially when belly tempered it makes for a nice, durable bow. I'm working on a shagbark hickory bow as we speak, and just finished tempering its belly last week. Tempering also helps with hickory's hygroscopic qualities.