Here's a list of things I've seen in most often in aram, and my opinion on them:
People afk'ing at the start of the game
---I. Hate. This. Unless you have a big problem that needs to be dealt with, please do not do it. It can actually ruin the entire game for your team because you forced your team into a 4v5 for no reason. Also, go to the bathroom before queuing up. You'd be surprised how quickly a game can start even when you've been on a "5 minute vs screen" streak.
"It's only aram."
---That is not an excuse. Don't use it. If you don't know what to build on champs, or what is the best order, don't wing it and go "well it's only aram" when someone questions your build.
----Same applies if someone suggests to stop going head first into the enemy team when your team can't follow up. Just because it's aram doesn't mean you can do whatever.
"I'm going to go ad/ap on (insert champ with no ap/ad scaling)" they say, as they get in game.
---Please make this known before getting into game, otherwise you're literally just trolling. If a champ has no ad/ap scaling, building those items on them doesn't work. At all. Ever. All you'll be doing is tiny, non-noticeable drops of damage and you will ruin the entire game for your team. I've seen this so many times, with only a few times where the person said "well i didn't know." If you seriously have no idea about a champs scaling, ask before getting into the game. Surprisingly, there's a lot of helpful players who play aram.
"I can't be punished. It's aram."
---And I have screenshots to prove otherwise. Just because you see others doing it and "getting away with it", doesn't mean they are or that it's not reportable. Aram is not a game mode that's safe from the rules. If you break them, you will be punished.
"The game is over, ff." They say at first blood.
---I see this more in aram then anything else. Please do not assume that first blood in aram means the game is 100% over. You'd be surprised how you can turn an aram around, even with a bad team.
People leaving because they think the game is over.
--- If people are literally spawning, do not assume the game is over just because the enemy team is at the nexus. I had a game where someone left because they thought the game was over when the enemy was at our nexus... even though 3 of us respawned and stopped them. If the nexus hasn't exploded, the game isn't over.
Pinging someone when the game just started or they've just respawned.
---If the game has only just started, doesn't mean everyone is in. Yes, some people will take an extra few seconds to actually load into the game. Mass pinging them just because you're already at the bushes wont get them to magically teleport to you.
----Same if they literally just respawned. Give them a second to actually start moving, or to buy an item they got the gold for as they respawned. Mass pinging doesn't give someone a magical teleport button. In fact, you're more likely to piss them off and make them sit there for longer or straight up afk just to piss you off. Don't do it.
"I can't ruin the enemy teams fun if I'm giving them free kills."
---Yes... someone actually said that once... in a game where the enemy team actually asked them to stop because they weren't having fun just sitting there because the rest of our team couldn't do anything. Take your enemies feelings into consideration. Surprise, some actually would prefer a fun 5v5 and not a 4v6.
"Stop talking to the enemy team."
---Aram is a fun game mode. Sometimes both teams have literal conversations. We do it because we can, and because we want to. Most often I see this done when someone on each team is dead. Heck, I once had a convo with an enemy when we both have 30+ second death timers because we were killing time while our teammates were fighting.
"Why did you execute yourself?"/"Stop executing yourself idiot."
---Why is it such a problem? If the enemy team is dead, I have a big bounty, and I'm able to execute myself, then why can't I do that to buy items and avoid giving the enemy team the bounty? Unless the person keeps trying to do/keeps doing it when the entire enemy team is up, there isn't usually any harm in it.
And my personal favorite, when I'm on my main champs:
"Why the fuck are we losing with the M7 Janna/Soraka/Sona on our team?"
---Because I can't save everyone, or you're doing the same thing as those on SR do: Running in when I'm not there. Just because someone got their main doesn't mean they can single-handedly carry 4 other people to victory.
What I do in these situations: Most commonly I report the person, depending on how they react/what they do. If they're doing something reportable, sorry, I'm not letting you get out of this match for free without a tick on your account. If they're not doing anything reportable, which isn't often, I just ignore them as best I can since there's nothing I can do.
Sadly, a lot of people have the "it's aram nothing can happen" attitude either because they keep getting away with what they're doing, they're following others thinking they won't get away with it, or they just don't care. Not much you can do about them really.