It most certainly does still take place on U.S. Navy vessels, to echo UncleBill and Tranquilis.
Similar ceremonies take place when crossing other notable “lines.”
I participated in a ceremony as my submarine crossed the Arctic Circle. The ceremony was presided over by “Boreas Rex, Ruler of the North Wind and Sovereign of all the Frozen Reaches It Touches.” After going through the requisite hazing, I became a “True and Trusted Ice and Brine Encrusted Bluenose.”
(The ceremony has been toned down in recent years, but mine still was pretty unpleasant and downright disgusting. For the Bluenose ceremony, everything revolved around cold, of course. I and the other “hot-blooded neophytes” were blindfolded, sprayed with near-freezing saltwater from the fire main, made to stand in intense drafts, and other stuff that I’ve blocked out. Very juvenile and fraternity-like. Yay team! :D)
Various outfits make up impressive certificates that crewmembers can purchase. One’s name is embossed with gold calligraphy, and there is even a faux-seal with the boat’s name and hull number.
The certificates usually list the date and other particulars of the crossing. However, because submarine movements are classified, all of these entries simply say Classified in the same gold embossed script. 
On the same deployment, we also received certificates certifying our reaching the “Domain of the Golden Dragon” as we crossed the International Date Line (impressive for a submarine out of Groton, Connecticut).
Other certificates include the “Golden Shellback” (crossing the Equator at the International Date Line), the “Order of the Ditch” (transitting the Panama Canal), and “Order of Magellan” (circumnavigating the world).
This website shows the various certificates available:
http://www.tiffanypublishing.com/certificates.html
Note that none of the certificates are in any way official. They’re just a personal memento.