All good advice. I've been commuting to work (on a cheap mountain bike) for about 4 weeks now, and by far, the hardest part is just deciding to bite the bullet and do it. My commute is 8.5 miles each way, on very flat roads.

What I have on my bike:
fenders, rack, lights, pannier/saddlebags, seat bag (for the light battery) and a pump.
I carry allen wrenches, tubes, tire levers, patches, and a very small adjustable wrench. I almost never use this stuff, it's just in case.

I bring in a change of clothes (jeans, polo shirt, t-shirt, etc.), a towel, a laptop, and every now and then I bring some food. Everything else stays at work.

It's not hard! The sweating isn't as bad as I thought it would be. I spash cold water all over my head and towel dry, and I'm good to go for the day. If you have long hair that might not be an option, but splashing cold water on your face makes a big difference when you're cooling down.