Military Mashup Machine: Oh, several. Examining them by the categories of the original trope, we have:
Land Battleship: This one, actually, they don’t have. Essentially, by the time it was practical to build this sort of thing, firstly, people who needed a heavy weight of fire on the ground were already in the habit of calling down the ortillery, either from the orbital defense grid or from an assault cruiser in low orbit over the battlespace – if they had orbital superiority. And secondly, anything like this that you did build would be a giant radiating target for said ortillery – if you didn’t have orbital superiority. Between them, these put paid to the notion of serious land battleships.
Submersible Carrier: Many wet navies have these, but they tend to be less the “plane-launching submarine” type and more submarines that can launch UAVs from missile tubes, control them for the duration of their mission, and then recover them at sea. Which isn’t to say that the former haven’t existed, but the latter are usually rather more practical.
Amphibious Tanks: All tanks are amphibious tanks, pretty much by default. By the time you’ve built a tank that can operate in all the various atmospheres, by composition and pressure, you might want it to (quick deployment and the needs of logistics sneer at air-breathing engines!) and incorporated the rest of the closed-cycle support you need to survive a modern battlefield in which nuclear, chemical, and nanoweapons are all in play, it pretty much shrugs off submergence, too. You can pretty much drive a modern Imperial MBT from continent to continent across the ocean floor, although I can’t imagine why you’d want to.
(Incidentally, since a very large number of them have some vector-control capability and/or nuclear-thermal thrusters, they also arguably qualify as flying tanks – which usage, however, is a fast ticket to a court-martial, since playing flying games with something whose speed and maneuverability is very much not equal to dedicated air vehicles is a good way to win the Expert Pop-Up Target Award for your next instantiation. It does, however, let you deploy your tanks with speed and convenience by kicking them out of the back of freight aircraft, and letting them ride their vectors to the ground.)
Amphibious Jet Fighter: Jet fighters, no, but we do have amphibious spacecraft – both certain shuttles common in orbital operations on worlds, water or otherwise, with extensive undersea development, and some types of system-defense vehicle whose ability to operate relatively deep in the atmospheres of gas giants – important to prevent enemy forces from field refueling, one way or another – permits operating in more terrestrial worlds’ oceans, which can be useful from time to time as a way to hide out and achieve surprise.
(It’s probable that gas-giant installation service vehicles and gas miners could also operate successfully in an oceanic environment, but there’d not be any point other than, well, saying that you’d done it.)
Mobile Factory: Even if you ignore the two hyperdreadnoughts with full on-board shipyards and the six Supremacies that act as semi-mobile bases for the fleets to coreward, rimward, spinward, trailing, acme and nadir, the Imperial Navy has to operate so often well outside reasonable resupply lines that it operates a large number of mobile logistics bases, large ships – with their own attached screens, parasite smelterships, etc. – which can be stationed anywhere to build new fuel, supplies, ammunition, and even AKVs to resupply task forces operating in their vicinity, using resources available locally.
And if we’re classifying the Cylon resurrection ships from Battlestar Galactica here, then we should also include the hospital ships – a historical designation – operated by large numbers of transsophont powers, which serve both as a well-protected place to keep the mind-state backup substrate, and also to house the large number of military-spec clone bodies used to resurrect anyone killed in action and send ’em back into the fray.
(If you manage to take one of these out, or even if you don’t, yes, this means that the number of bodies left floating around the battlefield afterwards bears no resemblance whatever to the number of people you actually managed to kill. Assuming that you managed to kill anyone permanently, which – since most militaries that make use of this particular technology offer off-line backups back at base as a service benefit – is, frankly, doubtful.)
The Battlestar: Well, as mentioned above in the specific trope of that name, there are several battlecruiser classes that are designed like this, simply because the on-board AKV screen gives them much greater flexibility when they’re out running patrols and such on their own or in small flotillas, rather than being retained as fleet screening elements.
And then there are the fleet carriers which carry around entire task forces between those star systems not linked by stargates, when necessary.
Others: While these do a good job of describing the main variations, there are plenty of other weird vehicles hanging around in larger or smaller numbers: burrowing tanks for special siege applications;
The Pindareth-class aerospace-support cruiser, a flying Macross Missile Massacre whose whole design function is to dump entire holds’ worth of bundles of air-to-anything missiles into the battlespace from orbit, then designate targets for them once they hit operational altitude, intended to swarm and destroy entire air forces in one giant orgy of nucleonic destruction;
And, on the personal level, a number of gunsword designs which, yes, turned out to be pretty useless as guns and swords both, but which, after being corrected to not throw off the balance and forgetting about the projectile, work great for extracting your sword from someone if you should get it hung up on some resistant bit of innards.