The most obvious: Ocean-Mage-Mountain-Warden. This combo relies on Vladimir, Syndra, Taliyah, Thresh, Nautilus, and Malphite--ideally building into Veigar, LeBlanc, and Brand.
This combo works fairly well. Ocean 4 gives your units a ton of free mana. Warden 4 (not hard to get a Warden's vest, but if you can't get the six mage dream, it's not hard to field a fourth warden) gives you a tanky frontline. Mage 3 gives your mages a chance to doublecast (and you can get the mage item to turn, sayyyyy...Malphite into a mage. Turns out that AP Malphite is just as devastating in tft as he is in League), and mage 6 gives you a guarantee that they do.
If you get a T3 Veigar, whose ability to instadelete non-T3s remains the same...well. He gets a ton of free mana and can doublecast so aint no MR in the world which can save the enemy comp, he still instantly deletes any non-T3 unit. (To be fair, in the current meta, it feels like a ton of people actually DO get T3 units.)
Mountain gives an absurd shield to a random unit. Vladimir is basically Swaine. Now, Swaine's ability dealt damage twice and healed continuously and targeted everyone, whereas Vladimir's ability deals damage to one target, healing once, and damaging once. So he's weaker. But there's a key difference. Swaine was a 5* unit. Vladimir is a ONE star unit.
A similarly strong combo is Druid Woodland Mage, building into basically the same comp. Not quite as strong in my opinion, but works just as well overall. Druids are basically a free Warmogs. Woodland can copy any woodland champion at the start of combat--minus their items unfortunately, but otherwise keeping their stats and synergies. Can be quite useful.
Thresh/Ivern both work similarly to Kayle--not actual invincibility, but with a strong shield to an ally, it makes allies virtually impossible to kill.
A combo which I want to make strong but haven't managed to figure out yet is Light 6. I heard from a stream apparently the way to go is to rush T3 on all light units and hope for a Lux and that your T3 Vayne is the last light unit left alive, but I don't know how well that will work since I haven't tried it out. I feel like playing through Yorick and building Light 6 Summoner could also potentially be good, but haven't gotten the chance to try it out yet.
I also know that there's a strong combo involving rangers, infernals, poison, crystal, predator, and a bunch of synergies like it (the comp had a ton of synergies, maybe had steel too?). Kog'maw was the key carry unit in that comp, but it was a comp that I didn't think of fielding because I thought it'd be way too squishy, a glass cannon comp dealing a metric boatload of damage but being able to be instadeleted.
Except they were still hard to kill. I wish I could remember the exact combo it had. Scarner, Ashe, Varus, Kindred, maybe it was Ezreal as the fourth ranger, with Kog'maw, some third predator (was it Rek'sai?), something like that. It's something which I can try playing around with at some point, though I do remember it took the infernal spatula item to get the infernal boost.
So, there are broken combos in the game already, these were just the ones I saw from like one day of playing.
I will say though: the ocean drake is pretty worthless since it's a one-time boost to mana at the start of combat. The mountain drake is OP since it's a permanent health boost to a unit and it doesn't take much to find a unit that is good on. The infernal one can be good; the cloud one is good when paired with defensive sparring glove items.
Speaking of items tho: they are basically a joke. Items are basically worthless, contributing virtually nothing to the combat. Combat is more decided by the innate attributes of the champions. Items have never made a difference in combat. Like, they might contribute to like...1% of a victory, or in the case of a Zephyr taking out your mountain unit by luck a 10% contribution to the victory off of luck, but the strength isn't in putting items on one unit or multiple units. The strength is in the synergies and the innate properties of the champions.
I've yet to see a champion who wasn't great without items be broken with items; I've yet to see a champion who with items performs notably better than they do without items. So, items are not very useful right now. That doesn't mean you shouldn't try to use them to their max. Broken items are still going to be good. The items which were good on Vayne are still good on her as she's one of the only units to remain basically unchanged; the items which were good on Brand are still good on him as he's one of the only units to remain basically unchanged; the items which were good on Veigar are still good on him as he's one of the only units to remain basically unchanged; the items which were good in general are still good in general as generic boosts.
It's just that items won't win you the game. They might help with like...5% of a victory, pushing a close fight which you'd normally lose into a win, but they won't give you a dominating lead.
Have to say, I am impressed and I am having fun.
There's a few comps I don't see any reason to really run (desert for armor reduction might be the intended counter to wardens, but wardens are never the carry units in a warden comp so I think that synergy doesn't add much; mystics might be the intended counter to mages, but the problem with that is, half the mystics are 5g units requiring level 7, a third mystic is 4g requiring level 5, you're not likely to get them and by the time you DO get them your comp is probably built in a way where you can't even use them--which is why, while mages might have a counter in the form of mystics, mages are still kinda broken because nobody ACTUALLY runs mystics because mystics are just too hard to get, to name a couple of them), but that was always the case with tft and will continue to always be the case.