I like easy, modern quilting lines. There is an example of curvy lines on the cover of Quilts and More magazine, Spring 2015:
http://www.allpeoplequilt.com/magazi...uilts-and-more
The lines can be much more casual also:
http://jeliquilts.blogspot.com/2013/...-festival.html
These could be done diagonally also, or as cross-hatching. You can find more examples by Googling "quilting curvy lines" and then clicking on "images". Lots of variations.
In all cases, it is very easy to do this type of quilting on a domestic machine using a walking foot. You simply pull the quilt from side to side as you sew to make the softly curving lines. I would spray baste for this technique, as it holds the layers together very well.