I have created this sign, but when I added the red texture to the face, the texture turned out sideways. Is there a way to rotate it? The original image is the right way up.
In the texture settings there doesn't seem to be a rotation value.
The way of doing it with simple (non-UV) texture mapping, is to tweak the mapping coordinate and scale.
But you see that it's quite limiting, less intuitive and flexible than UV-map based rotation, described in gandalf3's answer.
You need to UV unwrap it:
You should be able to rotate the UV map in the UV image editor with R to adjust the rotation.
See the wiki for more information.
Note that in cycles it's possible to rotate the texture without UV unwrapping via the Mapping node: