First and foremost, if you are with kids, be sure to take a photo of your child (or children) EVERY morning. Make sure you can see what they're wearing. This will come in very useful if you and your child/children happen to become separated in the parks. If this does happen, let a cast member know RIGHT AWAY and show him/her the photo. Disney has procedures in place for these sorts of incidents. Most times, someone just wandered off, but it's better to be safe in these situations.
Even the most experienced WDW guest occassionaly will get a cut or two. Accidents do happen, so it's a good idea to have a few bandages in a purse or pocket in case you or one of your family/group gets a cut. Keeping a few aspirin/Tylenol, etc. is a good idea as well, especially if someone get a little shaken up on an attraction and develops a headache.
Be sure to know where the first aid centers are located in case there is a bigger emergency.
Most especially during the warmer months (which for Florida means nearly year round) - be sure to use sunscreen and lip balm. It doesn't take long to get sunburned. If you're at the water parks, be sure to use a waterproof sunscreen and reapply when needed.
And most importantly, stay hydrated! Drink plenty of water! The last thing you want to deal with is dehydration. Stop at any drink kiosk and ask for a cup of ice water - it should be free.
Enjoy the parks - safely!