I've gotten my Mundo down to the point where I never have a "bad" game. I'm convinced that Mundo can't be forced out of relevance if played properly. What other champions are on par with him that can match his damage?
and 
are always relevant because of their CC. Plus Ori's kit is one of the best in the game
As stated above, both good suggestions. Ori has an amazing teamfight kit and a safe and solid early game. Ahri has a ton of mobility, CC, and good teamfight damage so she is viable in any meta. They can both can survive assassins as well as fight tanks.
Some other suggestions -
- This guy 'leaves' meta occasionsally (such as right now) but he's honestly not weak at all in current meta. In fact, you can even build him Cinderhulk and do just as well as most any other tank in the current meta. Especially since his passive helps a lot versus other Cinderhulk champions. Point is, even when J4 isn't the meta, he still works well enough to play.
- Always helps to know a lategame scaling champion. Kass has a ton of mobility and now he even has a decent laning phase. You can build him tanky or pure assassin depending on the meta and the role you need to fill for your team. This guy has never lost relevancy because of his ultimate alone.
- Arguably the best teamfighter in the game. He's a lane bully vs most with tons of snowball potential and insane objective control. He's difficult to learn, but if you do it's really rewarding.
- Massive escape, true damage on autos, lots of burst damage, excellent midgame, armor shred on E. Corki is probably the most reliable ADC you could learn.
- Now that they've buffed him back a bit this guy is quite good. I recommend Morello -> Stinger -> Deathcap -> Void -> Zhonya/Rylai -> Nashors with his current stats. Azir does well in assassin meta because of his shield and ultimate, he does well in bruiser/tank meta because he has so much DPS and peel. He's another difficult one to learn, but very rewarding.
are similar; they become a problem almost every game. I feel the same for my 
I rarely have a bad game. 
though is really scary (but not scary at all in lane). I only take ignite for mundo top, not even vlad. I think I have killed Mundo at least once every lane phase and first tower etc. I even end up zoning and tanking cleavers to deny him CS. Sometimes It's enough, but I've seen Mundos I gained 50+ cs lead over and a few kills run into my whole team slowly killing everyone and literally carrying. If he doesn't want to die he won't. is very similar to this, but much less defensive.
I'm curious do you got Smite/tp with 
?
always decent champs in the other roles;
Shiroi, it should block the q because If I remember correctly, the q is technically an enhanced auto attack.
Kassadin never seems to leave the meta haha. He's always been hard to deal with even after his nerfs. Lucian is very solid still.
I pretty much never have a bad game on 
. If you are ahead you are a team-tanking, team-melting monster. If you are behind you still have CC and tankiness to fall back on.
Oh, you mean specifically tanks?
isnt going anywhere ever, and he's actually very strong right now as a jungler. Also has good AP scaling.
has a great kit. He's strong as a tank right now, but he'll always be relevant with his ult and his dash.
has a great kit for fighting and does some %hp damage on top of his CC and damage reduction; I think he's going to stay relevant for a while, unless they really hurt his numbers.
Other highly relevant always champions:
(barring huge nerfs)
(his ult keeps him this way)
(very unique gameplay)
And others, I'm sure.
Without echoing any of the champs already mentioned, I think that 
will always be good no matter the meta because of his ridiculous split-pushing, dueling and team-fighting abilities.
