In multiplayer or LAN, I usually hide my stuff deep under the place I build my house or settlement. I never leave any tunnel between the surface and the stuff chamber because of people who use that xray addon to find houses on the map and grief them.
I don't play multiplayer too often, so I don't have a need to hide my stuff. But when I do, I just build a fake wall and put a chest behind it.
Honestly on most servers it's not a big deal, since you'll usually have the /lock command. If I didn't, however, I would use an enderchest and surround it with obsidian if needed.
I have a vault room down in the basement where I store all my precious blocks (diamond and so on). No one ever expects to find them there and I have a pretty big stash.
I use either an enderchest or simply place a chest and surround it by the area's blocks. Cover it with dirt or stone.
I have a treasure room right under my main house, they are all lined up and labeled. However the good stuff is hidden behind a wall you need to pickaxe down to get to off to the side!
Over a pressure plate hidden away somewhere. If they do find the chest there'll at least be a deterrent. I don't generally rig it cause I don't care enough, but it scares em anyways. Just blow em up the first time and they'll get it.
Most servers I play on have some kind of protection/property mod, so I'm set by just placing the chest somewhere on my land. It's stupid, I know, but that's about 90% of all the servers around my country.
For the most important items, there is no substitute for an ender chest. Most servers put a couple in their spawn for this exact reason. It's a perfect normal sized chest for all of your valuable items.
I usually have really elaborate storage systems composed of a bunchstorage mine carts and loads of minecart tracks. I have yet to lose any valuable items because no one has the patience to figure out how the system works.
I built a Redstone stair concealer. It pulls down the stairs to reveal chests which always works well if you can hide the control of it. I also added a combination lock to it to make sure that it's more secure assuming they don't just dig the stairs.
Usually I hide my stuff in the ocean. Simple trap door with a chest under it. No lighting and doesn't give it away, always worked for me!
I love hiding my valuables in what I'd like to think of a hidden lair. Usually I set up a secret door using Sticky Pistols pushing the walls open to a chest full of items. I either have a hidden Button or Lever somewhere that activates the Sticky Pistons via Red Stone circuits.
I always hide goodies in a mine connected to the house. We always build a mine right under the house and mine out all the resources. I choose a specific wall and store a chest in there with anything really good I find.
I used to hide a chest behind a light switch. No one thought twice about it and it was clearly marked when I needed to find it.
In servers that support teleporting to home, a friend of mine came up with the idea of cloud storage where he'd build a floating glass platform at ceiling height then put his chest there. He'd place it in the middle of the ocean so that there's very little reason for someone to look up and check since most people would be focused on searching for islands or potential underwater bases.
I have mine hidden underground. Not just anywhere underground... but you have to access a cave, hit the switch to open a passage, go down the stairs, find the other switch, then go down another set of stairs. Then hit a button that's hidden behind a waterfall, run to the other side of the underground house stand in the right spot to get dropped down into an underground river. Then you make your way to the bottom of that river to find the hidden passage that takes you one block down at a time to the bottom of the map. And THEN I have accessed my chests. It's a bit excessive, and there's nothing too valuable in there anyways. Lol.
I hide my important items in an ender chest for many reasons. It is impossible for them to take my items or destroy them but the only downside is that they are expensive to craft.
I probably can give you a million spots but I'll let you know where I personally hide stuff. Underground in the desert.