Powerpoint: animation to build a table, one row at a time

I would start with the final slide and work my way backward.

Create your finished table on a slide and then copy that slide and paste it before your finished table slide.

Delete a row from the table, and then copy that slide and paste it before the current one, etc.

As you go forward it looks somewhat animated (no flashy effects though) as you add one row at a time

This article (old article here) over at office.microsoft.com looks like it should achieve what you want, albeit via a slightly hacky method! (Copy and Paste special the table, in order to ungroup the table cells and animate them individually).

I used an approach where I created a table without grid lines but where the rows are alternating colors. Then I blocked off each row with a rectangle of that row's color. Then used the animation pane to make the rectangles disappear one by one, showing the text behind it. This is not super fancy but close enough for what I needed without a lot of hustle.