The question is how. Most people feel like they have to have a shower room at the office, and if you've got one, with janitorial service to keep it clean and towel service and lockers, I have this to say to you: "What company was it you said you worked for? Because I want to apply for a job!"
Then there are the rest of us. I for example have a company that provides an employee-policed shower room. Ugh. Better than nothing, but not something to get excited about.
And there's the unwritten observation about showers: they do take significant time. Figure getting in at least 40 minutes early to work, 15 minutes to cool down and 25 minutes to shower, towel off, change clothes, and hang up your cycling stuff. It works, but 40 minutes is a lot of time...
Then there's my solution: I use baby wipes.
Before you recoil in horror, let me walk you through my process. I cycle in to the office, and arrange the contents of my panniers. I cool down (I allow 10-15 minutes, depending on the heat of the day). I strip off my cycling jersey and hang it up on the back of my office door. Then I use two baby wipes, one for my pits, and one for my head and shoulders (hey, isn't that a trademark?) I use aloe wipes with a baby powder scent. (This may sound effeminate if you're a guy, but it's actually a quite refreshing smell.) Then, on with my working clothes, and I'm good.
The whole thing (including cool-down) takes 20 minutes max.
For a long time, I thought this was my own personal brilliant great idea, but one time I ran into a fellow cyclist at a hotel exercise room in Chicago, and found that he'd hit upon the exact same solution. So once again, I was humbled, as I am so often by this wonderful activity.
For an interesting perspective on sweat from the third world, go here.