The longest-running soap opera took a bit of looking around. I had believed it was likely to be the British soap opera Coronation Street, which has been running for over 47 years (since December 1960 according to a fan site) and is still running in the UK and in several other countries in Europe and North America. ITV, the network which produces the show, does not appear to have a special web page on the program, as far as I could tell, but has links to plenty of character-based trivia on the soap.
However, I do some further snooping, and the Americans have a daily soap opera, aired on CBS, called Guiding Light, which has been airing since 1952, making the serial 56 years old. Before television, it apparently was aired on radio as a 15-minute drama spot since 1937. So, if you count radio, then, the serial will celebrate its 75th anniversary on January 25, 2012.
The longest-running show on TV of any description of which I am aware appears to be NBC’s Meet the Press, a current affairs program which has been airing daily since November of 1947, making the program 60 years old on television as of last year.