A few options you can explore:
Exporting / Importing Fusion Comps:
As Boosuf mentioned, with a Fusion Comp open go to
File > Export > Fusion Composition.... You can then create an empty Fusion Comp in a new project and go to
File > Import > Fusion Composition... and any media referenced will also be imported into the Media Pool. This only really works with MediaIn nodes that reference a Media Pool source as opposed to a Timeline source though. This means don't create your Fusion comp on a media clip in the timeline but rather create an empty Fusion comp and bring in your media from the Media pool to build out your comp.
Using Power Bins:
You can drag a Fusion comp from the timeline into a Power Bin and you'll be able to use it in other projects. There's a big catch with this method though, any media that's referenced won't automatically import when you drag that Fusion comp from the Power Bin into a new project. There's two ways around this:
1. Use Loader nodes instead of MediaIn nodes like Boosuf mentioned. These nodes will reference the media directly on disk as opposed to a media item in the media pool. This gets wonky with H.264 files and some other file types, so it's best to use image sequences.
2. Keep all the used media for that Fusion comp in a bin, and then put that entire bin and Fusion comp in your Power Bin. Then, when in a new project, just drag that bin with all the media and Fusion comp out of the Power Bin and into your Media Pool.
Fusion Generator Templates:
You can save any Fusion comp as a generator which will show up in the Effects panel on the edit page. I've done this before for intro and outro graphics that are used often. With this method, you can just drag the generator to the timeline and edit it like any other clip, but it allows you to further edit the Fusion comp by clicking on the Fusion icon in the inspector. And you can even expose specific node controls from the comp on the Edit page for quick fixes. This method will also need to use Loader nodes instead of MediaIn nodes as it won't automatically import the referenced media.
Here are some videos about creating Fusion Templates: