Windows replaces copied item by the next item you copy which means you can just have one item in your clipboard. Now if you just want to increase that count and not a complex Clipboard Manager, xNeat is a great application. This application increases the count I have tried to any number you want and all you need to is to use a different hotkey when you want to paste.
Here is how it looks when you try pasting. It pops up the list of clipboard items and you can select any of them to paste it.
Overall this is an excellent app, simple and does its job. You can download it from here.