His signature character was a chatty taxi driver, which he played at least 20 times, most notably in The Maltese Falcon (1941) as a friendly cabbie who drives Sam Spade, played by Humphrey Bogart, during a mid-film wild goose chase, as well as in such other well-known films as The Big Broadcast of 1937, Lady in the Dark and Angel on My Shoulder.

His biggest role should have been the part of Gus Smith in the Alfred Hitchcock film Lifeboat in 1943.

Due to his becoming ill right before the start of shooting in August, he was replaced by actor William Bendix.

Frequently seen in comedies, Alper was featured in the Three Stooges films Tricky Dicks (1953) and The Outlaws Is Coming (1965).

One of Alper's least characteristic roles was the judo instructor in Jerry Lewis' The Nutty Professor (1963).