1. Sharp knives! Sharp knifes cut food with little added pressure. That means less pressure on the hand, and a lesser liklihood of slipping and cutting your finger. And, if you do cut your finger, the cut is super-clean and heals faster (take my word for it. I don't recommend cutting your finger, but after I cut myself pretty badly with super sharp knife, the deep wound healed in a couple of days without any, um, surgical intervention).
2. Always have a dry side towel, and don't pick up hot pans with wet towels. In our professional kitchen, we use side towels instead of oven mitts, and often these side towels are wet, from mopping up water holding peeled potatoes or drying damp hands. Sometimes, in a rush, I will grab a damp side towel to pull a dish out of the oven, and OUCH! Steam burn! The heat of the pan rushes through the damp towel and gives you a really nasty burn (almost as bad as no towel). Keep your dry towels dry and wet towels damp, and away from your pots. Which brings me to my next tip...
3. Have bleach on hand. In the event you DO burn your hand (or whatever), immediately pour undiluted bleach on that burn. It may hurt or look a little gray later, but I promise you this will help reduce the severity of the burn and help healing. You have to do it right after you burn yourself, not an hour or two later. After burning the back of my hand on an oven rack, this trick eliminated blistering and helped heal my burn.
4. While stocking your pantry, also make sure you have white vinegar on hand. When used with a wet rag to clean stovetops, any cooked on grime comes immediately off. Plus, it's relatively safe to use (no chemicals) and does leave a clean smell behind (compared to bleach!).
5. Place a damp towel under your cutting board -- so it won't slip when you're cutting that squash open.
Now that I'm in the tip-sharing mood, I'm going to put together some cooking tips. Please email your favorite cooking tips to email@example.com