Update 2017. Feb. 18.:
- Tested Minecraft Versions:
- 1.7
- 1.8
- 1.11
- Source Code:
- https://github.com/adventuretc/Itemstay
I recommend using ItemCase, as it saves items in a better way than ItemStay does and it uses player UUID's instead of plain text names.
https://dev.bukkit.org/projects/itemcase
ItemStay v.1.5.6 depends on ClearLag due to a mistake.
The plugin is a bit outdated by now, but still usable. Here is how you can install it:
Step 1: Download the latest ClearLag or the version that best matches your server version (I tested with ClearLag v2.9.3 labeled for Bukkit 1.10, running spigot-1.11.2-R0.1-SNAPSHOT)
Step 2: Download ItemStay v.1.5.6.
Alternatively, you can use older versions of ItemStay which do not require ClearLag.
The plugin doesn't support enchanted items and tipped arrows yet.
Summary
ItemStay allows you to drop an item and make it so that the item that you dropped cannot be picked up by anyone and will not despawn! Items dropped by users will NOT be stacked with the ItemStay items like they do using similar plugins.
Videos
Other videos:
(Portuguese)
Commands
Command
Function/itemstay
Create a new display. The next item dropped will be put on display./itemstay list
Able to be used by anyone. Shows displays within 5 blocks of you./itemstay delete <ID>
Delete a display./itemstay respawn
Find the ID of a display through /itemstay list.
Respawn every display./itemstay reload
Reload the configuration, reload the displays from file and respawn them.
Permissions
Permission node
Accessitemstay.admin
All commands of the plugin.itemstay.create
/itemstayitemstay.delete
'/itemstay delete <ID>' for displays created by you.
'/itemstay delete <ID>' for every display.
Support
Leave a comment or make a support ticket for help with the plugin.
Plugin now cross-released at Bukkitdev.
http://dev.bukkit.org/bukkit-plugins/itemstay/
Compatibility
The plugin should be compatible with pretty much any version you might be running, including 1.7.x, Spigot 1.8, 1.8.8, etc.
Credits
garrett2smart87 - plugin inspirer, manager
nighteyes604 - plugin author
adventuretc - maintainer, developer
Source code
You can find the source code inside the .jar file.
The source is also available on Github. Feel free to make a suggestion.

ItemStay (old) 1.5.6
ItemStay allows you to make item displays with items that are impossible to pick up.