How about in 1 24 hour period?

Swaziland-South Africa-UK-Germany.

Switch Zagreb to Rijeka, Trento to Trieste, Eindhoven to Maastricht and Kolding (DK) to Padborg, and it's just 21.5 hours:

http://maps.google.com/maps?f=d&sour...cht+to:padborg

And in theory, that's just enough time to squeeze in Malmo, Sweden as well:

http://maps.google.com/maps?f=d&sour...richt+to:malmo

So that's Croatia-Slovenia-Italy-Austria-Liech.-Switz.-Germany-France-Lux-Belgium-Netherlands-Germany-Denmark-Sweden, or 14 countries in 24 hours, and the route above is suboptimal because it detours into the centers of the waypoint cities instead of driving past them. Also note that all borders except Croatia-Slovenia are within Schengen!

Your routes don't include Austria, however it should be easy to include Austria in these itineraries.
Furthermore, now that I am nit-picking, Liechtenstein has not yet implemented the Schengen agreement and there is border-control-via-video at the Swiss-Liechtenstein border.

In a 24 hour period I flew Buenos Aires>Santiago>Lima>NYC

The people who work on the boat traveling between Buenos Aires and Old Colonia, Uruguay get to see those two countries multiple times a day. :)