Mark Ovenden spent some time of his talk discussing subway logos and how most countries around the world actually use the letter M for Metro or U for Underground as their logo or the initial letter of the subway's name. The London Underground logo or roundel seems to be one of the few exceptions to this "rule".
From Edwardian times, transport operators quickly realised the power of logos and how the logo should try to convey speed, reliability and safety. The logo was mainly used to identify where the subway station was, as in the main, entrances to subways are holes in the street taking the commuter down some stairs to the underground. The logo therefore, was used to prominently point out where the tube station could be found.
St James Park (the station where the London Underground's head office still is), started testing a variety of logos in the early 1900's. The "Bullseye" was rolled out from 1908 onwards. However for a while the Metropolitan and District Lines used their own "Diamond" version.
However, the roundel that we are used to today, didn't come along until the 1920's and utilised the brand new London Underground font which Edward Johnston produced in 1916 - the familiar Johnston Font, which we still use today.
Also, the London Underground is pretty unique in that we are one of the few subway systems that use the logo as part of the station name sign.