I used to commute in my work clothes some time ago, my commute was shorter then. If I was to do it again I'd keep some spare stuff at work for when it rained. I didn't back then though. On one occasion that I got really soaked I spent the day wearing an old boiler suit and some safety boots while I dried my stuff in an incubator.
I am planning to do that when I start my new job next month, but for now I'm just office temping so it's not really doable. I'm just glad I'm doing the temping in summer, it would be awful if I turned up looking and feeling like a drowned rat every single day.
Edited to clarify: I plan to keep spare clothes at work, not to work in an old boiler suit and some safety boots.