Experience From - Mike Franusich , Ray Zirblis , Blake Wood , Robert Thomas , Simon Shadowlight ,
Assuming there are none of those Sierra Nevada bears that rip open car doors to eat the leather seats...
I've had good luck with caching food/water by burying the stash bag under a pile of rocks. I also make sure I can triangulate to the cache from easily recognized landmarks, even in the dark.
For shorter term stashing, I like to put my water in a big ziplock bag, then I can just fold up the bag and take it with me. A little duct tape over the seal helps keep it closed and also can give some indication that the bag hasn't been tampered with by some joker.
Make sure to hide it well, or else some well-intentioned hiker is liable to clean up your "litter".
You can also mark the cache area with the universal animal "this is mine" scent (pee on it).
Depends on the critter and terrain. Hanging by throwing a nylon cord over a tree branch is good against most any animal if done carefully, in my experience. (Any animal except man.) A basic outdoor book will show you how. In coniferous forest or upper elevations with stunted growth, a cord between two trees can work as your 'branch.'
People-proofing requires the extra step of choosing a tree off-trail and a container or stuff sack of a dull color. Map the location, or mark the spot where you need to step off trail with a cairn.
If you are just going to hide food in reused plastic containers, try rinsing them out with bleach solution first. At higher elevations, caching in snow is OK as long as you bury your food pretty deep--at least a couple of feet. Ravens will dig through a foot of snow. Cairns can work above treeline.
Do map and mark as necessary. In my experience, memory can't necessarily be trusted to remember caches. Identifying features may change quickly--leaves may sprout or fall, snow may arrive or melt away. Ten paces east of "the large boulder" may fail you in a boulder field full of them.
In bear country, I've also cached plastic bags of food by weighting with rocks in a stream at times, but I can't say if I've just had luck or if this is a good approach. Hope this gives you some ideas.
Several people have mentioned the standard trick of hanging food from trees. It is worth noting that in many parts of the Sierra Nevada backcountry, backpackers are explicitly instructed NOT to hang their food anymore - the bears got too smart, and can nearly always get hung food. Only the bear-proof containers are allowed now.
A few years back when my Dad hiked the John Muir Trail, we stashed some food a few weeks ahead of time by soldering it into a coffee can, which we left near Muir Pass (well above timberline). This might work well if all you have to worry about are mice, squirrels, marmots, and ravens - animals that might chew through a ziplock. Probably ought to wash the outside of the can carefully, however, to remove the food smell.
Blake (who learned the hard way that bears can get food hung from trees)
There is one fairly fool proof way to easily safe guard food and that is to use a heavy duty plastic bear proof canister. They can be purchased through mail order or locale camping suppliers. Just fill it up with what ever you want and hide it somewhere off the trail. Even if an animal finds it they can't open it.
Hanging food in a tree is very iffy; many many people have lost food that's been hung up in trees.
One camp area I stayed at had a warning sign from the locale ranger stating that he would give you a ticket if you did hang your food in a tree. There was a bear in the area very adept at getting food out of trees.
Hiding food under rocks is also not very safe unless it is only cans or other containers that have absolutely no smell. Anything repackaged will have some sort of lingering smell. I once spoke with a hiking group that hid their food bag by covering it with rocks, two feet under water, in the middle of a stream. A bear was able to find their food and steal it. The bear smelled some oils seeping out of a leaky plastic bag I suspect.
If you don't want to spend the money or can't easily recover the bear proof container. Hanging the food bag is the best bet. If you want to be safe you need to get the bag very high off the ground (20 feet plus)). The line needs to be out very far on a thin limb (no more than 2 inches round at end), far from the main tree truck (10 feet plus).
I previously worked in the Sierra Nevada Range and was amazed at some (most) of the bear-hangs people would attempt. The attitude frequently seemed to be "as long as it's off the ground, it's o.k." I recall being with one group and placing (what I thought) was a good hang. The bags were roughly 15 feet from the ground, away from the trunk and large branches, and on a branch that I didn't feel a bear would venture on to. We awoke that night to a sound that can only be describe as a "frustrated, bellowing demon from hell" echoing through the valley. We trekked down to the food bags and saw what I'm sure was momma bear at the base of the tree.
"Are the food bags safe"?
"Yeah, their all there".
"Wait, what's that? Shine the light above the bags... that's where the noise is coming from".
Suddenly, from "I shudder to think how many feet above" , baby bear (one of two it turns out) takes a kamikaze leap from a larger branch at the food bags. As he (she?) sails by, he grabs at them, slashes 2 of them and proceeds to land on the ground amid a shower of food. The family proceeded with their casual grocery shopping while we debated whether or not it was a good idea to attempt to scare off a mamma and her cubs (FYI: the flying baby seemed none the worse for wear).
So, back to the original question: I would echo that your biggest consideration should be, based on the area your running in, what can you reasonably expect to need to protect it from. If your on Forest Service or Park lands, you should check to see if they have specific requirements/recommendations. Bears really are hard to protect from... an adequate bear-hang is a piece of work. My preference (in non-bear areas) has been to bury under a pile of rocks, avoiding "large holes" so that the little critters (especially marmots and chipmunks) can't get through. Of course, the previous comments about marking it and hiding it from other humans are important as well.