In a Views template, how can I mimic the effect of "Link this field to its taxonomy term page"?
One easy-ish way to do that within the Views UI is with the option:

"Rewrite the output of this field"


Add term id field Check "Exclude from display" 
Order the field so it's above the other fields 
Edit the field you want to convert into a link 
Check "Rewrite the output of this field"


e.g 

&lt;a href="/taxonomy/term/[tid]"&gt;[name]&lt;/a&gt;


to create a link.

You can also add a global "Custom text" to add arbitrary text using the replacement tokens there as well.

In that way, tokens from your view fields can be made available as replacement pattern options in your View.