There do not appear to be any depictions from Roman or Greek times of what I've heard some refer to as the forearm handshake. But there are examples of our current-day handshake being depicted in both cultures.

Here is a an Athenian grave stelai from around 402BC depicting a handshake between Hera and Athena: http://commons.wikimedia.org/wiki/File:ACMA_1333_Samian_decree_2.JPG

There are also even older Greek depictions of Hercules on vases, including this one: http://www.theoi.com/image/K5.6Apollon.jpg

And as far as Romans go, here is a coin depicting an agreement/handshake: http://i.stack.imgur.com/LCP4h.jpg

I realize I haven't provided an exact answer for you, but hopefully this helps a little.

Edit: You may appreciate this: The Significance of the Handshake Motif in Classical Funerary Art by Glenys Davies

Seemingly not - most Roman iconography concerning handshakes, such as surviving wedding/betrothal rings depict the hands shaking in our modern, conventional way (e.g. http://www.edgarlowen.com/a55/b7789.jpg , http://media-cache-ak0.pinimg.com/736x/35/51/cc/3551cc3bdf0f1045137b994f1c2998d5.jpg ). Which is a shame because the 'Roman handshake' is gnarly as hell.

What about the Hitler salute thing? I remember seeing the Rome TV series than they would thump their chests and do a Hitler salute. How accurate is that?