A lot of supports will probably fit that bill, like Braum, Thresh, Leona, Janna. The team will always need initiation/peel. Damage supports are fun, but the ones more traditionally suited to the role can always work, regardless of possible nerfs, whereas damage supports are easy targets for assassins and may not fit well with your team comp.
For mid lane, I think Lux is another example akin to Oriana. She has great range, the shield, snare to catch people out and scales pretty well into the game to deal tons of damage, especially in close quarters (and who doesn't love a good brawl in the jungle?). I also feel like Fizz can be useful in almost any situation and is probably the only classified assassin you could add to this kind of list. His laning game may vary greatly in difficulty, but he has enough tools to avoid battles that aren't in his favor and he's one of the only assassins who doesn't have to be super fed to engage on his own.
Some top laners could prob be given the same regard as the support role. If they have CC and/or are tanky enough to engage, then they'll always have a spot on the team. Darius may receive nerfs now and then, but I feel he's still pretty balanced overall since a missed grab destroys his engage ability and he needs to be in a fight quite awhile in order to get those dunks off. He's usually my go-to top laner. Yasuo was designed to always be useful with his Wind Wall (I remember reading some of his release design notes stating they wanted the W to make him helpful toward his team even when behind) and scales hard with room to go bruiser or assassin, so whatever bans or nerfs come his way, he'll still probably be a good pick. (I still play him mid even though I'm adding him to the Top section here.)
Some ADC's seem to go in and out of style, but I still personally feel that come late game any one of them can still be meaningful. I suppose requiring late game and possibly some peel might take them out of the 'always viable' spot, though. Tristana might still be a worthy addition to this list, though. The range, siege potential, and self-peel on her ult and jump are great for any game.
For junglers, I'd say those who can fit the top/support description should be relatively safe bets. The dmg meta game for this role seems to vary pretty often. Someone like Lee will always be a contested pick, but he requires a team and good mechanics. I think the ones who can always be useful, though, are Amumu, Rammus, maybe the new Warwick (love the rework).
That's all I can think of for now. I'm not sure if you were fishing for more ideas or just curious if anyone else one-tricked a champ, but this is what I'll leave you with lol. Personally, I tend to play Malzahar more often than anyone else. Who needs meta and viability when you can be the Prophet of the Void?
mid pretty much since I started in S4. She's always worth playing, never nerfed because she's such a fair champion, and is useful on pretty much ANY team. I haven't been able to find another champion I can consistently play in another lane who doesn't occasionally get nerfed hard or who requires a certain kind of team comp.
. I've never seen him be BAD, and he can switch between fighter and assassin pretty easily in his build while still bringing big CC.