Who are the best and worst champions when behind?
Which champs do you think are the best and worst to be if they get behind? My nominations:
Best:

Worst:

Which champs do you think are the best and worst to be if they get behind? My nominations:
Best:

Worst:

Your worst champions are actually not that bad since they can easily rebound back if their team isn't just outright crushed (Riven gets some gold from RRing the enemy team, probably also a kill, Diana can kill squishies with her combo even when behind, and Katarina can just stay safe and wait for resets) And get back into the game to still be relevant.
I'd say the worst case I've seen is
- You got camped and fed? good luck doing anything later in the game as a melee champion with horrible skill damage, unreliable escape/cc and a steroid ult which doesn't help in any way when behind.
Best would probably be
as you said, always relevant because of the grab and cc chaining, also
who can just go in ult and die and STILL be usefull to the team in that way that it wins them the teamfight
From my own experience...
BEST
Top:
Jungle:
Mid:
ADC:
Support: Basically everyone but Sona, to be honest.
WORST
Top:
Jungle:
Mid:
ADC:
Support: 
No one mentioned Cassiopeia
is pretty useless when behind
- still very effective even when behind
dats why u should not nerf rivens snowball potential or she is useless and then people cry about 0/10 feeder riven in team
: Good luck being useful if behind. In my experience you aren't even a good stun bot.
: Actually has decent wave clearing potential when behind. Really she's my goto ADC if I don't feel like trying new ones.
Good when behind:
Bad when behind:

has to be one of the best
I'd argue against Blitz when behind, his picks get harder and he has less potential when the enemy is stronger. He generally ends up with 1 target that he can pull and cc if all the enemy is fed. Blitz is only good when he has fed his ADC and is ahead, otherwise his pick potential simply becomes extremely weak.
Good when behind: all cc bots like

and bad obviously goes to assassins:

A caveat for champs like leona and blitz. When you are behind in lane as either, you are very weak in lane. If Leo is behind, then she dives in and dies. All of the pressure she provides in lane is by threatening a dive. If that threat is not credible, you might as well not exist. Of course, your cc can still be valuable defensively and is great in teamfights, but in laning it is important to stay ahead as leo. In contrast, a Janna who is behind will do just as well peeling for her teammates.
Likewise, Blitz can really struggle when he is behind in lane. Sometimes there are game when I am against a blitz as support and we are winning lane and I WANT to get pulled because then he has given me an engage for free (for example if I am leo).
very true, but CC is still CC, and when behind, Leo at least has the option of being a very defensive cc bot so her ADC can get away and possibly turn the engage around. Blitz doesn't have the same luxury, one cc doesn't compare to all the cc leo has.
Also most any Support who doesn't need items to get their job done should easily top this list. They're used to having negligible amounts of gold and being effective, so it should go without saying that they would perform better the farther behind the bar is set.
Worst:
(Get instabursted)
(No damage --> useless)
(shes always bad)
From my experience (he ones I play) Worst Swain: (he has no burst dmg anyway, without being fed he can't even heal enough to survive)
Renekton: Kinda like pantheon, if he's behind, he'ill have no damage but won't be tanky either, since he's more about a burst combo, and not dps dmg (like most fighters), he can't 1vs1 anyone if behind, while other champs can 1vs1 adcs and supports easily, even 0-5)
Best: CC champions pretty much. Even tho assassins are supposely bad when behind, I can always recover from a bad lane as Talon, once I get hydra, i can use W hydra active to clear an entire wave and get lots of farm, also I can always kill isolated squishys targets, since he can still kill with 1 combo, even behind.
Best:
Still has a ton of utility and can turn fights with a good ult, 20% damage reduction on a target can make up for your team being behind
can build as a kite mage and be incredibly slippery so you are able to deal decent damage even when behind and has one of the best pick tools in the game with E.
just needs to be in the right spot late game to get the resets and bring her back into the game
just turtle it out until you become a late game monster
Best
Worst 
Best: Blitz, Thresh, Irelia
Worst: Cait, Nasus, Kha'Zix
i would say all assassins are pretty bad when behind and really good when ahead