It all depends on you and also your goals. I used to run in the army early in the morning and do the whole push up sit up thing. As for balls to the walls heavy lifting (which is what I do now) I feel stronger and can lift more when I lift around 3-5pm and have had a few meals
Even training on an "empty stomach" should still be done with a little bit of food. ie, a glass of fruit juice and a handful of aminos. You need a little bit of something to get your metabolism going in order to optimize the workout effects.