From reading alot on the fitness forums, MANY people do cardio(in the morning mind you, without food for 8 hours or over) without eating first and there are some who feel sick and dizzy if they don't eat so I guess it depends on how much of an impact it has on you. If you do feel sick, then maybe eat an apple or something a half hour before your workout. Me personally, I can't workout on an empty stomach so I prefer to workout about a half hour after a light snack. I tried this before and I was getting tired really quickly and quit half way through the workout.
For strength training, I suggest a high protein low carb meal before hand, like about an hour and a half before the workout but if your not hungry at all and feel comfortable enought to do your workout, then eating is not necessary, like don't FORCE yourself to eat.....but everyone has different opinions on this.