If you are creating your own handle from scratch, a few caveats.  First as mentioned, you need to pay strict attention to growth ring orientation and grain straightness.  Second, if you want to use some nifty looking wood species such as oak, walnut,  cherry, mahogany etc. follow these instructions:

A.) Take the bare hammer head over to your hammering partner.

B.) Drop it on his right foot.

C.) Ask him "If this were to happen again with the head traveling at 100 MPH and the jagged wooden remnant of the handle were to perforate your foot and stake you to the ground on this spot, would you find it pleasurable?"

If he says "Oh my, yes" go ahead and make your nifty looking handle.  Otherwise use  ONLY hickory or osage orange (Also an archery wood).  Third, don't cut your handle blanks.  Splitting follows the natural strength of the grain and produces a far stronger handle.  This is the one time when it's alright to use a handle that's a little bent (I mean a little) or wavy, since these defects in a split handle do not significantly impair strength unless you try to "pretty" it up and sand or cut it straight again.