No, the base is not closed. A poorly researched article in Popular Mechanics started this rumor in 1997. The author failed to meet his "contact" in Rachel, then got lost in the desert and ended up at the gate to Bombing Range 61, some 20 miles from the "real" Area 51 gate. He mistook this remote, locked gate for the gate of the "closed" Area 51 and came up with the absurd story that Rachel had been deserted, Area 51 closed, and all projects moved to an abandoned missile launch site in Utah. Click here for more information and photos of the alleged "New Area 51".
In reality, Area 51 is not going anywhere. The base is well alive, with over a dozen daily Janet flights between Area 51 and Las Vegas, transporting an average of 1500 workers each day. Also, the white bus that brings in workers from Alamo and other nearby towns can be seen regularly going in and out on Groom Lake Road. A new runway was added in 1992, another one in 2001, a taxiway in 2003 and new hangars in 2004 and 2005. The base is expanding, and all indications are that one or more major new new projects have in fact recently moved into the southern area of the base.