You saw the Garland line, which opened in 2002.  It's supposed to be extended several miles to Rowlett in 2012.

The 27½-mile southeast-northeast line opens in 2010.  Another northwest line, actually west-northwest, should start running in 2011 and be completed in 2013.  

I don't know of any city that has a regional peripheral rail transit line.  Certainly not New York, Chicago or LA.  The only place I can think of where something like this is being built is the Petite Ceinture tramway around Paris.  The French are further ahead than anyone on transit development.

London has the North London Line which, while not technically rapid transit, has a level of service close to it with electric commuter trains running every 15 minutes or so. LA has a "suburb to suburb" commuter rail line, the Inland Empire-Orange County line of Metrolink, which is reasonably popular, for a commuter rail line anyway. And Washington is looking to build a suburb to suburb link between two rapid transit lines. And LA also has the Green Line, which is a fully grade separated rail line going from Norwalk to Redondo Beach, not passing through downtown, so I guess that can count as peripheral too.