How can I create a library of animations? I want to store animations (just the animation data itself) so they can be recalled and reused in other projects.

How do I create such a library of purely animation data?

(For instance if I have some text animations that I like the feel of and wish to reuse)

I can see why you might flag this as possibly answered the question though the suggestions are not quite what I meant, I want a library that is visible to all projects without 'linking' akin to Photoshops presets.

In fact I wish this was the case with all data objects, materials textures etc.

EDIT
Please see the edit. I wasn't asking about linking files, but about libraries, so that animations appear as presets - this should not have been marked as duplicate especially in the light of this.
Blender allows you to link or append.

Linking only creates a reference to the cross-referenced object.

Appending imports the cross-referenced object into your current file as a local copy.

Both are available through the File menu.

There's a great answer already on this site:

How can I reuse existing materials, objects, etc from an existing .blend?

Presets

So in response to your updated question I understand that you want something accessible from all projects without linking.

This is where add-ons come in.  There are loads of them out there and if you know (or are willing to learn) Python then you can roll your own add-on.  There are plenty of examples out there and here on how to go about this and also the source code for the included add-ons are available on git.blender.org.