I'm looking to replicate the SharePoint taxonomy functionality in Sitecore - there is the ability in SharePoint to type a new value in a multivalue field and it would automatically create the new taxonomy value on save. Is there a good way to replicate this functionality in Sitecore? Will this require a custom field?
Yes it will. There are no field types that ship out of the box, that gives you that functionality.
If you are going to explore making your own customisation for this, I would suggest the
Multilist with Search field is a good place to start.
A good place to start could be: Have a Field Day With Custom Sitecore Fields
I've used the
Inline Item List field in the past:
It provides extra buttons to create items from the
Multilist field so that you don't have to leave the item you are editing. It hasn't been updated in a while so I can't speak to it's compatibility in Sitecore 8+.