running to work?

It depends what facilities you have and how often you do laundry.  I second the weekly drive with to swap out laundry.  Carry as little as you need to.  Lights and reflective gear is extra important especially when running in the dark and the rain.  Commuters just don't look for people.

 Have a back up plan for those days when things fall through (late meetings, injuries, sickness ) while you're at work without a car.

In the shower?

I bike to work, and I do the drive-in once a week to carry in supplies.  Typically, I'll keep two suits and dress shoes in my office, then just carry a clean shirt, socks, etc., in a backpack each day.  Friday is casual (read: jeans), and it's a pretty casual environment to begin with, so khakis work just as easily as a suit.  Lots of flexibility with regard to attire and a shower on-site really help make this a no-brainer.

X2

I did this for a while while out East. The only problem was that I worked about 12 miles from where I lived. I would run out with a track bag on my back carrying the basics and then take the metro home. Because of the distance, I only did this 3 times a week. On Fridays, I would actually run both ways. My office was great though because it had a small shower in the basement, and I arrived earlier than everyone.