You can't crop an image to anything but rectangular, because image files are always rectangular (even with ImageReady). You can use a vector masks so that the corners of an image are transparent or anti-aliased to a background color (or other underlying images or objects), however.
You can acheive the effect you're asking about, though.
1) Add a white rounded-corner rectangle to your document and adjust its size and position to what you want. (I will usually set the opacity of an object down for this stage and then turn it back to 100%.)
2) Select the rectangle and your image.
3) From the menu, select Modify > Mask > Group as Mask.
Note that your original image is not modified, the mask only acts as kind of a window frame and can always be undone. If you wish to crop your image to the visible portion, you can use the menu item
Modify > Canvas > Trim Canvas.
You can use any vector shape to create a mask with, including text shapes. A white mask causes the underlying object be fully opaque. Black or transparent areas in the mask cause the underlying object to be transparent. Grey or partially transparent areas in the mask cause the underlying object to be proportionally transparent.
Thanks, that works perfectly; great solution!
Masks are really useful things and it's worth spending some time playing with them. You can use images as masks, too, and you can get some pretty interesting effects sometimes.