As some have said, I've only heard bad of aspen and pine. I think ash, maple, juniper and hazel are all appropriate for flatbows, which is what you probably want to make.
What sets flatbows apart is that their limbs are rectangular in cross-section.
Another popular type is the english longbow which is typically long as fuck and heavy to draw and almost always made of yew. This one typically has D-shaped limbs (in cross-section).
Traditional Bowyer's Bible 1 and 2. Has almost everything you need to know.
http://www.mediafire.com/?26sdzs1ql4viylchttp://www.mediafire.com/?hzh6mb4c1ciykteThe trick is to keep one growthring intact spanning the entire back of the bow. The back is the side facing away from you when you draw.
Image is a tiny (110 cm) juniper recurve I made for a kid. It was my second creation. My first shattered, deafeningly, on the tillering stick.
In the future I think I'm sticking mostly to takedowns (usually 3-part bows where the limbs and riser are separate, though there are 2-part takedowns aswell which are adjoined in the handle). I've been thinking about buying exceptionally straightgrained, thick, long and wide hickory axe/spade/sledge handles and cutting them into strips to use as backing for juniper limbs. Good or bad idea? It seems like the best way to acquire hickory at a reasonable price in the swedish backwaters. Hickory is supposed to make a great backing strip and they say juniper's good in compression...