Technically, you're not supposed to use an article in front of ship's names. You wouldn't say, "The Robert is on his way." You'd say, "Robert is on his way." So it is with a ship. So, while VOY and ENT were breaking with Trek tradition by calling their ships simply Voyager and Enterprise, they were actually using correct grammar.
I frequently (usually?) hear the article -- at least in normal press and common usage.
Just as an experiment:
"The Ark Royal" - 24,400 hits
"The Akagi" - 13,100 hits
"The Sovereign of the Seas" - 14,200
"The Great Harry" - 30,700
"The Redoubtable" ship - 65,600
It should be pointed out that the usage of the article is just like in other languages.
"La Santissima Trinidad," "La Nina," "Le Bonhomme Richard," etc.
Tony