If you're flexible, there's no problem. You *definitely* won't go hungry! If there are any places you have your heart set on, you stand a good chance of being disappointed if they're filled up that night- you know the hot ones- Cali Grill, CRT, Le Cellier, Character meals *anywhere* really, 'Ohana, 50's Prime Time, etc.
Remember you can try and make ADR's when you get there, too. Let's say you try for 'Ohana one night and it's packed and you go elsewhere, you can always try for the other remaining days availibility as well. Also, you can try and make an ADR in the morning when you are at the park you choose.
If you still try to wing it right up until meal time, you'd be best off dining earlier or later than most people instead of at the most popular times.
There are also some great counter service places. If you familiarize yourself with those names, you can *always* get a great meal in the parks, even if all the table service places are booked.
Some of my favorites are:
Epcot: Fountainview Bakery, Tangereine Cafe, Yorkshire Fish Shoppe
MK: Pecos Bill's, Cosmic Ray's, Columbia Harbour House
DAK: Tusker House, Flame Tree Barbecue
I've also had a good quick meal at the Wolfgang Puck Express at DTD. Beaches and Cream at BC doesn't take reservations and I really want to try the burgers and ice cream sundaes I hear so much about.
If you are staying at a resort that provides room service, that is always a wonderful option and I've found those meals to be the same quality as the resort's sit down restaurants.
If you are staying moderate or value, don't order room-delivery pizza. You would be MUCH better off calling a Papa John's! It is simply terrible. Much worse than the food court.
Some places that you might find easier to get into that aren't counter service:
Trail's End Buffet at Fort Wilderness
Plaza at MK
Kona Cafe at Polynesian
Enjoy your trip whatever you decide!