1. Always wear the PFD around the water
2. Review rule #1 and make sure it is adhered to religiously
3. Only go near the water with adult supervision
4. Fire safety - never walk between someone seated at the fire and the fire, always walk behind them
5. Never stray far from the campsite alone
6. Always have a whistle clicked onto your belt loop to be able to signal for help
7. Everything else is fair game...have fun and be inventive

My kids have only been once or twice, and are age 12 (very soon to be 13) and 15.  They have some general camping experience, but Algonquin Camping is a bit different.  I find it works best if I explain the "why" behind the rule.  Please don't wear shorts there you'll come back with cuts all over your legs (and get eaten alive).  Dry clothes = clean clothes.  The sun is blazing, wear a hat/sunscreen.  If you are using your knife, don't walk, that's a quick way to a bad end.  Jackets don't stay out overnight unless you like soaking wet jackets.  Muck is deeper than you think it is.  That helps them participate in their own safety and comfort.  I know a lot of these are just assimilate-to-camping kinds of behaviors, but I'll add one more to that - kids are very unaware of dangling sleeves and long hair when it comes to proximity around fire.

The big ones to me are more when exploring around or away from the campsite:

1) If you go exploring for a little while, fine, but remain within whistle-shot and stay together. (and they know that 3 sounds = distress signal)
2) We all wear the whistles 100% of the time.
3) Make some noise as you go so you don't surprise something large that has a bad sense of humor.
4) Watch your step, there are lots of little crevices, etc., that you can't see well.
5) Keep your eyes open.
6) Never trust your footing on wet rocks or logs.  They are not your pal.

Things like #4 and #6 really are worth making note of to the kids, at least with my kids.  Simple safety prevention things that they just wouldn't be aware of because they lack the experience. 

This year, I'm planning on letting them take the canoe out to do a little exploring, but I'll be controlling the where and how far part of that pretty closely, some of which will be determined by the lake we're on.  I'll be working with them this summer in advance of the trip.  I want them to develop and feel some independence in this, that's where their fun will come from, but I need to equip them for it and place intelligent boundaries without being overly restrictive about it. 

Make up a small safety kit for each kid. Trying to remember off hand what’s in the ones I made the kids. A small knife. Matches. Small lighter. Fire starter. Bandaids. A couple water purification tablets. I put them in water proof case like the size of a wallet so they have them all the time. Clip it to the life jacket or in the pocket of the life jacket at all times on day trips.

Last year I took my three boys(two 5 year olds and a twelve year old) back country.  First of many I hope!  Everyone had whistles on lanyards.  We also brought walkie talkies which was nice to let them explore a bit while I got some camp chores done.  

Some good ideas,
I go for a walk around the camp area with the kids to get the lay of the land and make sure there's no surprises.  I give them a perimeter boundary (usually just past the box) to stay within.
With small kids, you can expect that they'll spend most of the time falling over roots etc..  a pair of kid-sized leather gloves saves a lot of scrapes and puncture wounds and solves the inevitable tree sap issues as well...

after 20 years of taking hundreds of kids into the bush, I agree with all the above, but would add a quick-clot sponge to your kit, along with a pack of steri-strips, and some burn GEL (not cream).
a couple of things to add- what goes in the fire STAYS in the fire; it's not pleasant when a burning brand snaps off and goes down someone's back! Same thing with marshmallows- burning ones STAY over the pit until out! and no "hunting firewood" alone, use the buddy system!

Baby oil for tree sap ... man oh man I needed that tip about 5 years ago ...
Be sure to share the story you said of a close call last year ... might save someone from having a similar experience .. .

@deadweight and paddleindad : I'm sure you could use baby oil to take off pinesap safely off a tarp or tent, not sure though if it would leave a stain? Not totally sure if toilet paper would absorb the oil totally if you rubbed it? That I never tried.

As for busted toenails on kids feet, my young son ( at the time) seemed to hate wet feet in sandals, so kept kicking them off, promptly stubbing his big toe and totally lifting his toenail off when he ran around and tripped. I luckily had a small canister of tar salve, bought at a nearby native reserve, the salve was to prevent infections. Carefully treated the toe,Wrapped the toe in a lonely bandaid and all was fine. The salve however, was known forever after as ' the stink pot' because the smell was enough to send anyone running. But it always worked as a charm on many many trips, on any scratches, open wounds etc. I was never able to buy another canister unfortunately. What I currently see in drugstores has only a 0.05 percent tar rate ( baby section) . Mine had 2 1/2percent tar. However, the lower amount may work just as well.