Alistar does best when...
Taric does best when...
Soraka does best when...
Lulu does best when...
Sona does best when...
Jana does best when...
Thresh does best when...
Blitzcrank does best when...
Leona does best when...
I know there are more champions that are played as support, but I believe these are the ones most commonly played in this position.
Alistar does best when...
you want to keep harm away from your carry, especially vs "dive in" assassins like kha
Taric does best when...
you want to play a very aggressive botlane, but still want to have the fall back pattern of turtling it out if things go south.
Soraka does best when...
when you want so annoy your opponent till he gets to aggressive and punish him for that. Also when you play certain matchups and need the mana (works well with e.g. urgot and graves), also nice in AoE-Ap teams for the sustained shred
Lulu does best when...
you want to peel for your carry and poke the opponent out of lane early on
Sona does best when...
you can utilze her AoE-speedbuff well, and you have good follow-up on her ultimate or need the AoE counterengage
Jana does best when...
you really want to peel for your carry/reset fights (like e.g. if the opponent has only one engage like a shyvana ->blew her away and poke again or chase)
Thresh does best when...
you play a pick-comp or really need the lantern to keep an immobile adc alive in clashes
Blitzcrank does best when...
you want to snowball hard
Leona does best when...
you want to snowball vs a squishy lane like sona...or if you lack engage in general.
Nami does best when...
you want a really versatile support that can trade well in lane and offers incredible follow up on engages/very good dis-/counterengage
morgana does best when...
you want to block certain abilities like vis ultimate with your black shield to keep you carries from harm
...
soraka does well with urgot. Lulu is a midlaner atm leona does well with draven thresh deos well with almost anyone. Janna does well with Kog
sona does best when solo bot lane from start lol, cant tell you how many games I carried bot as sona vs a duo n won. or how many games I would do 99% of damage n others would be mad that I don't let them ks me when im a sup sona. ur only and ADC if u actually are the ATTACK DAMAGE CARRY. so if ur champ damage totals are half mine, ur pathetic as an adc n should never complain about ur sup when they have to carry you for a bot win and game win. there are games where I fully carried, led and tanked as a sona for a game win. SONA is a champ that is so vastly underrated its crazy. With a sona in first two tiers, u don't need an adc, and if u get one that is garbage, just makes it harder for u to carry.
Alistar does best when...Blitzcrank wants to be cool, and pull Alistar in. Only to get a Q-W in the face.
Thresh, and leo are the best right now. They both can take ALMOST anyone just fine. Both are playmakers also, love those playmaking supports :)
Honestly, it's all about the adc choice. A person chosing an adc should think about what their support does. I've seen many a bot lane fall due to somebody picking 
with his support being 
. If your adc relies on pokes, get a support that pokes as well. If your adc does lots of burst damage, or relies on autoattacks, get a support with heavy crowd control. Also, don't be afraid to think outside the box in terms of supports. You'd be very suprised how many champs are viable supports in the new meta (great supports in my opinion 
.)
