I can't imagine not showering if I had one available to me.
Like Hydrog33r I have a full set of toiletries (including a double edge razor, shave stick, shave brush and aftershave) and a towel at work. I carry clothes back and forth but that's it. I do have a pair of shoes at work on a full-time basis. If I need to swap out the towel or restock toiletries, there's generally space in my back pack or I do so on days I drive.