Well, that depends on the kind of ship.
And there are other ships, that do not fold neatly into one of these categories. Please add only examples that do not fit in one here. (Such as falling into more than one. Or sailing through dimensions and the like.) If you're still not sure, consult the Travel Cool vehicle index.
If you're looking for a relation-ship, please see Shipping Tropes.
- Mazinger Z: Salude and Bood, Baron Ashura's submarine fortresses. The former could disguise itself like an island.
- The Dai Gurren in Tengen Toppa Gurren Lagann. Although it eventually gets the ability to swim and fly, it was originally designed as a land-based battleship.
- Specifically it was designed as a fully-functioning Humongous Mecha with a battleship for a torso.
- The Mother Vanguard from Mobile Suit Crossbone Gundam - it's a Cool Starship that's basically a mecha-scale pirate ship, complete with beam sails for propulsion, a full-body beam shield and a golden figurehead of a woman on the prow.
- Space Battleship Yamato deserves mention for being a cool ship that was sunk and later converted to a Cool Starship.
- The Bardanos from Ozuma which is basically a cool sand submarine.
- In Harry Potter and the Goblet of Fire, the Durmstrang students travel to Hogwarts in a submerged sailing ship with only the crow's nest visible, but dramatically bursts up out of the water when it arrives at the school.
- In The Silmarillion: Eärendil's Vingilot. It starts out as a fairly Cool Boat and ends up a very Cool Airship / Cool Starship...which also happens to be the morning star.
- In John C. Wright's Chronicles of Chaos, Amelia has Vanity summon her Cool Boat in outerspace. It surprises Vanity, but turns out to be a Cool Starship as well; they go to Mars (the planet) in it. Amelia also sees others sailing through space in what are clearly Cool Boats.
- International Rescue had a whole cool base full of cool ships on Thunderbirds.
- The TARDIS of Doctor Who. The most powerful ship in the universe- Bigger on the Inside, sentient, can travel anywhere in time and space....and stuck in the form of a blue police box, and so old that it's pretty much held together by string.
- The titular battleship Antaeus from Hostile Waters: Antaeus Rising is the last functioning capital warship, preserved in case war ever returns to threaten humanity. Not only does the ship survive being sunk for 20 years (albeit some damage does take some time to repair), it is also capable of literally creating armies out of junk.
- There were 2 such ships kept at the bottom of the sea. Only the Antaeus managed to surface again.
- In the TIE Fighter series, the Missile Boat. It is regarded by all fans of the series as the prime example of More Dakka and in X-Wing vs Tie Fighter, it was left out for balance reasons, but it still had an entry in the craft library that reads: "This is the King Hell God Emperor Starfighter of Death and you can't fly it yet!"
- Shin Megami Tensei: Strange Journey has a ship class all on its own, comprised by five ships - the Lightning, the Red Sprite, the Blue Jet, the Gigantic and the Elve. How cool are they? They have VTOL capabilities. Despite being essentially several-story high, massively shielded tanks. Equipped with plasma armor. Fabrication laboratories. Hospital sections. Its very own on-board AI navigator. And dimensional-crossing tech.
- The Lightning is even capable of recreating hostile dimensional terrain to better suit the navigator's needs.
- In the PC-98 Touhou game Phantasmagoria of Dim. Dream, the final boss Yumemi and her assistant Chiyuri cross into Gensokyo from an alternate world with a Probability Space Hypervessel.
- Yellow Submarine. The yellow submarine isn't just a Cool Boat—it can fly. It also has its own Hyperspace Arsenal controlled by Context Sensitive Buttons, and the 7th Cavalry standing by in case of attack.
- The Godzilla Power Hour: The Calico is essentially an Expy for Jacques Cousteau's Calypso, but with a fast hydrofoil mode when it really needs to get somewhere. In one concession to reality, the Team Pet, Godzooky, usually has to take to the air to reduce the weight on the ship in order to reliably maintain this form of propulsion.
- The Essex class carriers. They were fast, carried lots of planes and there were 24 of them. Working together they could sweep the air defenses from large islands and even archipelagos.
- Iowa-class battleships. Generally considered the best of their kind ever laid down, they fought not only through WWII, but also Korea, Vietnam, and even Desert Storm, where their massive firepower persuaded entire companies of Iraqi soldiers to surrender, rather than try to withstand some 20,000 pounds of Explodium raining down on them every 45 seconds from a ship so far away they couldn't even see it.
- The Independence-class littoral combat ships. 418-foot trimarans that look strangely similar to the Daedalus-class battlecruisers from Stargate SG-1. Only one of the planned 12 has as of yet been completed - the USS Independence (LSC-2). They're in competition with the Lockheed Martin's Freedom-class littoral combat ships, which look more conventional. Two have been completed so far out of planned 20. Interestingly, the two classes are in the same registry category (LSC), except the Independence class has even numbers while the Freedom class has odd.