I have a Brother sew/embroidery machine that sews sideways and diagonally, as well as front and back.

Baby Lock also has directional sewing

My Vikings do, even the one that is really old. My Brother NQ3500D does, its a middle of the line emb/combo. It even has a foot that you can attach and have it trim seams as you sew like a serger. I'd never get rid of my serger but its great that these machine companys are thinking ahead

The Elisimo made by Babylock does this. I love to use it for patching and sewing on name tags. I have also used it for attaching logos on a letterman's jacket.