A flexible, but rather slow approach is to use the Alt + A keyboard shortcut for “add tag”, and to make use of auto-completion when typing the key and value. That approach (or presets as mentioned by PHerison) is good for normal mapping, i.e. when you map lots of different objects.
You can also copy and paste the tags from an existing way. Select the tagged way, press Ctrl+C. Then select as many other ways as you want and paste the tags with Ctrl+Shift+V.
But when you are drawing a large number of one particular type of object (e.g. unpaved unclassified highways), I believe the following is the single most efficient solution:
1. draw all the ways and *leave them untagged for now*
2. Ctrl+F, search for **type:way modified untagged** (this selects all untagged ways you have added or modified during the current session)
3. add the tags to all of them at the same time
I guess that’s unlikely to be supported in the near future. As a rule, highway=unclassified tend to be paved in many (most?) developed countries, and JOSM doesn’t have country-specific assumptions built in as far as I know.