you need to mask it with an "alpha channel" or export a "path". you can also save as a ".gif" and select transparency (white matte)... there is also the ".png" option, this format also supports "transparency".

as for using the crop tool to eliminate the white background, you can get as close to the circle as the square will allow but you'll still have the "corners" to deal with.

what do you want to use it for??
is it for web?
do you just want the white gone so the underlaying layer is seen in the same Photoshop file??

let me know so we can give you a better "less-vague" answer ;)

:)
retrocity