Gragas works very good as support imo. He's tanky, he has a slow, small stun and a hook which is all easy to hit. And they are all AoE!
Q - Does damage and slows the enemies (in an area/AoE) so in team fights he can actually slow multiply enemy champions at the same time.
E - Does damage and stuns the enemies for just a little while, you can also stun multiply enemy champions that gets hit. Also good to save your adc or other team mates if they are getting killed since E is quite easy to hit. If you also have Q ready they will eat a slow aswell and you will continue to damage the enemy...
It can also be used to rush and block your adc from other abilities hitting her.
R - In early/mid lane game he can use ult to either make enemy champions (adc) to get closer to you and your adc, so your adc can get a kill, in other words it works like a hook, which is easier to hit than thresh's or blitz's hooks. Or if you and your adc has low health and getting chased, you can ult the enemy champions away to escape.
General: Often enemy adc and support will stick quite close to each other, when you engage with "Drunken Rage" (W) before hitting "Body Slam" (E) and lastly end with "Barrel Roll" (Q) combo, you will do nearly same amount of damage to both adc and support since all of your spells are AoE. So if you have damage, go for it, and your adc will follow up if they get damaged enough and get kills. And shortly your adc will get fed and be as fat as you ;)
Caitlyn: If you're working together with Caitlyn, a good thing is to throw an ult if the enemy champions has low health so the support and adc will scatter away from each other so Caitlyn can get a free ult to kill without the enemy blocking one another.
Graves: Me and my friend (and some randoms sometimes) has played Gragas + Graves bot which is a TANKY and good combo, mostly eaten all our challenge at bot.
Gragas has alot of CC's, but since his CC's doesnt last as long as the majority of other supports, he would suck as support if he doesnt do any damage. His spells doesnt do mad damage overall, so its pretty easy to damage the enemy alot without accidently killing the enemy yourself (even tho he bursts quite good with the W+E+Q combo) and to give your team mates the kill instead. Thats why he's alot better with some AP items so he deals damage at the same time he's CC'ing the enemy team constantly.
Over and above his CCs in spells you also have the Summoner Spell: "Exhaust" and the item "Frost Queen's Claim" which is good slows. And buying "Randiun's Omen" will give him even one more slow/CC.
Always go "Ionian boots" since he has cool down on all his spells. After using them all you'll walk around a few seconds worthless, so "Ionian boots" (10%) and "Frost Queen's Claim" (10%) gives cool down reduction which is very important for Gragas here.