Say you have something like this:
glBindTexture(GL_TEXTURE_2D, my2dTex);
glBindTexture(GL_TEXTURE_1D, my1dTex);
glBegin...
What is the correct
I think that the 1d texture will be drawn. As far as I know, each texture unit can have only one texture bound at a time. The number of dimensions of the texture doesn't really come into it.
To have more than one texture bound you have to activate more than one texture unit (using glActiveTexture), like this:
glActiveTexture(GL_TEXTURE0);
glBindTexture(GL_TEXTURE_2D, my2dTex);
glActiveTexture(GL_TEXTURE1);
glBindTexture(GL_TEXTURE_1D, my1dTex);
This comes from my knowledge of OpenGL 2.1 though, so please correct me if they've introduced some fancy new texture extension in a later version!