"As the crow flies"
An old sailing term. Ships unsure of their position in coastal waters traditionally released a crow, which would fly towards the nearest dry land, thus giving the vessel at least a rudimentary navigational fix. The tallest lookout platform on a ship, from which said crow was observed, was called the "crow's nest."
"Olly olly oxen free!"
Shouted at the end of a game of hide-and-seek, it lets all remaining hiders know that they can emerge safely. Though there are many variations on this phrase (such as "all ye, all ye, all's set free"), it's probably a corruption of a German phrase, "Alle, alle auch sind frei" (literally, "Everyone, everyone also is free").
"Cut to the chase"
We can thank inexperienced silent filmmakers for this one. Many early films (and come to think of it, contemporary films) climaxed in chase sequences. If a film was hampered by extensive and laborious exposition thanks to a cut-rate screenwriter, producers would often ham-handedly fix the problem with an abrupt "cut" to the chase.
"On the lam"
"Lam" comes from the Icelandic "lemje," meaning "beat" or "thrash." Thus, "on the lam" and "beat it" mean approximately the same thing: to run away; to beat the ground with your feet.
"Over the top"
A World War I-era military phrase referring to trench warfare. In order to launch an attack from a trench, one had to go "over the top" of the defensive parapet and into the line of enemy fire. Here's a haunting (and rare) color print of French soldiers in a trench, circa 1916: