Textures can be created using various different methods. The first of which is line. When a line is diagonal, it gives a sense of excitement and movement. Eyes follow lines. This can be interpreted as movement. Where do you want your users eyes to move?
Diagonal lines tend to imply movement. Varying the thickness and direction of a line will generate even more movement and character.
From a design point of you, boxes that have rounded corners will soften the layout and give a more organic feel. It also makes websites less formal.
Something that has come in more and more with the advent of CSS3 is rotation. Rotated objects break up horizontal layouts and, in the same way as rounded corners, make things feel more organic.