Rounded corners in Cadsoft Eagle
In Eagle, the "Dimension" layer represents the perimeter of your board. You can create a new board perimeter by drawing an enclosed shape using the WIRE command to draw a new enclosed polygon. When you draw your lines, you have the option of changing the wire bend to go straight and then arc (option 6 and 7). I used a width of 0 for the shape.

When you go to export the design, you can export the outline separately or on a existing layer. For example, BatchPCB suggests adding the outline to the silkscreen layer, or having a separate outline gerber. 

I'll second Kellenjb's comment that not all board houses are thrilled at the idea of arbitrary board shapes, so you may pay extra for the rounding.