What if you train on an empty stomach? Is this bad to do? I get out of bed at 5am and head right out. Then I don't eat anything until 9am when I get to my desk.

Also, sometimes I forget to bring water with me when I bike/run. In addition, when I get home, I get so involved with walking the dog/getting ready for work, I forget to drink something to rehydrate.

Are either of these things really bad?

depends what you want out of your workouts, and how quickly you want to progress thru and into your workout goals. Eating a carbo-protien combination within 30-40 minutes has been determined to rapidly reduce recovery times. (how's that for alliteration?) But it's true. At least for me. I always try to have something in my stomach within a half hour of any decent workout. I've had workouts (mostly runs) where I've burned over 2000 calories at a go (this according to my heart rate monitor formulaic estimate). I'll come back very hungry and wanting to eat something immediately. Eating during the workout helps, but I don't normally do it. I probably should. If it's a midday workout, and I've forgotten to bring something for lunch, I'll hit the vending machine for a snickers or something. Perhaps I'm revealing too much about my bad habits. But the candy bar is just enough to keep my stomach happy until I can get something afterward.

this is a good article on breakthrough workouts. these are ones where you really want to eat something afterward:
http://www.trifuel.com/triathlon/triathlon_training/000433.php

the training bible has a good section on nutrition as well, and covers the arguments for eating after workouts.

I totally agree with what tdb said - I do the exact same thing. I eat at least an hour before working out (something high in protein - a bocca burger with an egg usually). During workout I replace protein and carbs with accelerade (better than gatorade because it has protein in addition to carbs - as tdb said it has been proven to help in recovery time - which I rely heavily on because sometimes I do two two hour workouts in the course of a day). Then I eat within 30 minutes of a workout too. Eating is soooo crutial to improving performance and giving your body the energy it needs to do what we put it through.
I have noticed really nice muscle definition as well as speed and endurance improvement since I have been paying such close attention to what goes in.

Thanks so much for the info TDB and Tri-Me! I'll check out the article and read more about workout nutrition.