Is there a way in Eagle to make it route power and ground traces thicker, and signal planes in some other width with the auto router? Or if I need different trace widths do I have to route the board by hand?
You should route critical nets like power and ground manually, even with good autorouters. The Eagle one is very poor.
Leon
You can find a dialog box called “Net Classes” under one of the menus in the schematic editor. There you can create new classes and select the minimum sizes and separations for each class. Then, in the editor, click on “change/classes/[your new net]”, and click on the nets you want to move to the new class. The auto router and DRC will do the right thing.