after we've got a gank, pushing the wave is important.
something that I'm often iritated by, is when I'm playing passive and farming, and suddenly my support seems to get bored or antsy and makes an obviously bad engage. I mean, I usually can appear passive, and will jump into action when there is a good engage of course, but like. like the wave was slowly pushing as I was farming, and so I clear out the wave with 1400 to back, but then my support decides they're bored or something and headbut combo's the enemy and does OK damage, but then now we are near tower so have no way to kill, but having used half our cooldowns we just gave the enemy a huge opportunity to kill.
so I guess the takeaway from that really is: think about kill potential of an engage, and also think about cooldowns. not every support can poke very well, and if you can't poke very well, you need to be conscious of being careful what you do in a skirmish. like, for an alistar v thresh lane, the alistar should skirmish if the thresh uses q, whether or not thresh lands, but even then he has to be aware of the minion waves and adc positions. if the enemy adc or minion waves can do more damage to alistar than the allied minions and adc can do, it isn't worth engaging for alistar.
so
- minion wave size/content (melee does less than castors does less than canons)
- adc positioning (and, do either have a dash)
- support cooldowns
something else that irritates me is when the support randomly leaves. I like when supports ping red or yellow pings right before they leave to ward, or leave to collapse for the jg/mid. there's been times when I'm focusing on last hitting a minion, the support leaves me and I don't notice, and within 2 seconds I'm out of position and hoping the enemy support doesn't collapse on me by the route they couldn't have taken while me support was there.
something similar that I don't really know how to explain, is using the zone. when I am csing, if the enemy is pushing the wave, or if the wave is pushing into us, I need to be using autos every chance I can to counter the push... but if my support isn't using their threat of abilities to keep the enemy from harassing me, then I can't auto the wave and the wave crashes under the turret and we lose lane a little each wave until we're behind. but the right way to zone is very skill reliant, and requires a lot of experience with matchups between 4 champions.
then there is supports csing while adc is walking to lane... very sensitive territory. to be ideal, sometimes it is actually necessary for the support to push, for the support to last hit, or even for the support not to take minions at all because last hitting is actually pushing the wave slightly. IMO, do whatever you feel is right as a support... as an ADC I've prettymuch come to accept whatever happens to the wave while I am gone and IMO that is the right mindset for the adc. but since you asked "what is your favorite thing supports do" well one of the things that I get all impressed about is whenever the support makes the right call on how to handle the wave xD it's a tough skill to learn for an ADC who needs to focus on this, so when a support does it right I smile a little.