Anivia - my main champ and I hardly see people using her :3
Zilean - dont see him much in rift, dominion a lot - and fail a alot T_T
Nunu - dont know why but I dont see him a lot.

Karma is really weak as support :/.

When i play ranked and say I want to play support karma, people will usually rage. Her heal just isn't good enough

I haven't seen many leonas lately. Idk why, i think she is a great support champ.

Some other champs I don't see much of are: Zil, Mao (unless its free week), anivia, and kog (unless its free week).

I'd say Katarina. Against reasonable cc, all you have to do is get your timing right in a team fight. Also, her ulti is useful for detecting stealth units such as Teemo, Evelyn and Akali.

Sivir also tends to be underplayed as she doesn't have ahe's stun/arrow, vayne's tumble and insane damage, or caitlyn's insane ragne. To be honest she is average, but still fun to play.

I also barely see any Pikachu these days, he is definitely an underplayed champion. But that is because Kenen is currently outplaying Pikachu in almost every single ways. I hope he will be buffed next patch.

Gragas def fits the bill. He's got a high skillcap since his main nukes are all skillshots, his dash is not a typical blink but has a low cooldown and requires precise control to not fail going through walls. Quite a few pro players use him fairly often, but he gets less and less play the lower your ELO is.

Anivia too, she has one of the few aoe stuns in the game and is a big mana hog, her wall is also tricky to use. Her mobility is on the low end and her passive can be either misused completely or pull off epic first bloods. A lot harder than say, Ryze, Ahri, Kass, etc mid.

Twitch is also underrated and hard to play. He has some success as a jungler due to his ganks and can make enemy lanes play passive due to his stealth, but you rarely see him anymore.

Play as support doesn't necassarily always mean healbot. Her W is nice because if you cast on an ally (assuming the two of you are well organized), you can net up multiple enemies at once. Cast on an enemy, it's a slow, obvious why this is useful for a support. She is a good support, just don't try to play her as if she was soraka or something. Sure her heal is weak, but her abilities are too useful to other players to lane her alone.

EDIT: Wait, I get it, NM.
I am no expert on Karma, but I would never build her as a support. I think I would build her AP (right guys?). But playstyle? It is nice to have other players there to take advantage of her stuff.

Leona is so OP.. 3 stuns the second not being a true stun but still stops a champ.. its impossible to not get owned in lane without being zoned and if you know how to counter her please tell me because i play her all the time and have not been succesfully countered not once

Good counter to leona is alistar, He packs just as much CC a heal which rivals sona and sorakas so long as you have mana, and his ult will let him survive through leona's CC barage.

Never really see Zilean, Heimer, Kharma, Eve...

Karma is just bad, not misunderstood. Eve is terrible.

Heimer and Zilean do what they do alright, but there are almost always better options for what they do.

Zilean

Trundle

Karma

Sejuani

This is a real shame, since these are some of the better (in my opinion) heroes. Zilean has some incredible buffs, and a great Q, which will either secure the kill, or bring them low enough for your WW or whoever to finish them off.

Karma has a lot of capability to be very powerful, yet people avoid her like the plague for one reason or another. My theory is that it's because she's so balanced. Yeah, she has a lot of great spells, but they're nothing extraordinary. Though that's why I love her. People don't see her, so they don't know how to counter her. Also dat shield.

I've seen my fair share of bad trundles. Which is extremely depressing, considering Trundle is one of the strongest characters I've seen. His ability to rush in and out of a fight whenever he wants really sets him apart from the rest who have to rely on flash or similar spells.

Sejauni has some beautiful CC. All those slows are a great mix with a Zilean. Sejuani moving 55% faster, hitting a group of enemies, slowing them, double time bomb, then slowing the support or carry down by another 55%. Devastating.