In a moment of reckless abandon, I decided to clean my white MacBook today. I wash my hands almost every time I use my laptop, but oil from my hands still builds up and attracts dirt. This leads to very irritating grime. Ordinary water won't due the trick, so I decided to tempt fate and use something with bleach. I'm pretty sure that voids my non-existent warranty.
I sprayed some Easy Off BAM Multi-Surface Power Cleaner with Bleach onto a damp paper towel and then rinsed out the paper towel a couple times. I squeezed as much water out of the paper towel as possible, and then I wiped my keyboard, etc. clean. I didn't put the cleaner on the screen--I'm not that brave ;) Then, I took a microfiber towel, wet it, and wiped down the whole laptop. Then, I used a dry part of the same towel and dried it completely.
The wet microfiber towel always does a good job with the screen. The cleaner did a great job with the grime. Some of the keys are still shiny (presumably from hand oil), but it's now very clean. I performed the entire operation without turning off the laptop.
So far so good. I'll post an update if my laptop suddenly melts tomorrow or if the dirt returns within a week.