A quick note this list most definitely contains SPOILERS
I figured that a list of what each character like/dislikes to hear in terms of conversation stances would be supremely helpful for a handful of the achievements, most notably anti-social.
Also, handlers have separate bonuses depending on if they like or dislike you, so don't be worried that you'll lose them if you have bad rep.
Here's what I know for sure so far
A quick note for here, if you're using the recruit or veteran background, selecting those choices will usually lead to +1 rep
Likes-Professional, sometimes suave, usually the options will only give positive rep if she already has a good opinion of you. Completing bonus objectives in some missions will get a +1, completing the Rome CIA listening post, NSB hotel, and Subway station levels with no civilian casualties also makes her happy.
Dislikes-Pretty much anything else, mainly aggressive, killing civilians in the NSB hotel, subway station, and agents in the CIA listening post will piss her off A LOT. If you're going for anti-social this is a good way to get her to hate you.
Likes-Casual/Suave, basically just be friendly.
Dislikes-Aggressive-Insult him and claim to be a better agent and you can get some negative rep.
Likes-Professional/Aggressive, lines that basically get straight to the point, also listening to him after the training course and going more in depth about his job will net you a +1
Dislikes-Suave/Cocky, insulting or mocking him and being dismissive will get negative rep.
Westridge-A combination of Aggressive and Professional seem to be his favorites. When you get to Saudi Arabia you can immediately switch off the video feed for some funny lines and -1 for him.
Likes-Well sparing his life that's for sure, listen to what he has to say and agree to work with him and he'll send you intel over the course of the game, use the "Contact Shaheed" option under the buy-able intel before the roman ruins mission for a +1 later.
Dislikes-Aggressive and dismissive lines, sparing his life but basically ignoring what he has to say or his intel will get negative rep.
Likes-Aggressive, agreeing to help in the train yard, as well as having fought/killed Marburg in Rome earlier will give positive rep, bash on Marburg any chance you get.
Likes-Suave/Casual, basically don't be to uptight when you first meet him, choose a lot of the options, sending him weapons from the train yard as well will get a +1 rep and some funds a bit later
Dislikes-Well smashing his head definitely isn't good, being professional and aggressive will get him to dislike you, if he hates you enough he will sell you out to the embassy and the guards will know you are coming.
Likes-Professional, not much more to it than that
Brayko-A very minor character in terms of how his reputation affects you. You can't get any positive rep. After the fight, if you have the right dossier info on him, you can get him to tell you about Surkov via the "dossier" conversation choice, which you need for access to the 2 achievements "Russian Alliance", and "Price for Lying". You can do this without that info by choosing the professional stance
Likes-Spare her life and let her go and that will give positive rep, she should give you a locket, mentioning the locket to albatross will give him -1 rep
Dislikes-Not much, aside from killing her there aren't many other options to interact with her in a negative way.
Likes-Professional, Sparing Al-bara in the Sniping mission will get you a +1 when you first meet him, Getting him to like you is needed for the "Respected Enemies" achievement.
Dislikes-Suave/Cocky/Joking, Killing Al-Bara in the Sniping mission will get you a -1 when you first meet, as will helping SIE in Moscow. You need him to dislike/hate you in order for him to fight to the death and get the "Youth Trumps Experience" achievement. From what I can tell he needs to be at least -7 for him to stick around and fight.
Likes-Professional, sometimes suave, having her help you during marburg's villa should get you a +1
Dislikes-Aggressive, if you act like enough of a jerk she should run off from the safe house, and if you choose to save her instead of disarm the bombs she gets angry and leaves.
Likes-Professional, be direct and to the point, agree to help
Dislikes-Cocky/Suave, if you find the right Intel during his mission you can blackmail him and that will get you negative rep, as well as lose his support option during the final Taipei mission.
Likes-Casual, agree with him and play along with his antics and he'll be happy, tell him to cause a huge mess of a distraction at the hotel and thats another +1
Dislikes-Professional/Aggressive, basically call him an idiot, respond to his emails with sarcasm and contempt, tell him to not hurt any civilians at the hotel. Also do not erase his data during the same mission, that will get you another -2. You need to have bad rep with him for the "Never Trust a Sociopath" achievement, it doesn't have to be at -10 like the achievement description might have you believe, but it does have to be pretty sour, if you've done it right the achievement should pop after the final Taipei mission when he contacts you about the assassination.
Likes-Professional, spare him and work through the dialogue to reveal that you were both misled.
Likes-Suave, forward her the emails you intercept for her stories, each one will get you a +1, select the professional line when she asks what to do in the NSB hotel mission for a +1 as well.
Dislikes-Aggressive, during the first meeting on the plane pretend to be a oil business man for a -1, in the Taipei hotel mission select the option to have her seduce and that will get you a -1.
Likes-Varies, professional mostly, sometimes aggressive, whenever you have the option to "bluff" take it. Be really straightforward, usually he likes the aggressive choice when he asks about a choice you made on a mission.
Dislikes-Suave/Cocky-Be really evasive, or just silent a lot and you can get negative rep.
You need to have a good rep with him for him to offer for you to join Halbech in the end which is needed for the "Rising Star" achievement.
Likes-Agreeing to work together and sparing Sis, also in the Taipei mission, you can remove the bug on his server for a +1, but you can also bluff and pretend to remove it for the same +1 but some additional intercepted emails.
Dislikes-If you kill Sis that's a big -2 right away, if you act flippant about it (the choices) he will like you even less, if you keep bringing it up and mocking him about it then then rep is gonna sink even lower, keeping your bug on the server during the G22 Taipei mission will get you negative rep as well.
I'm sure there are some I've missed or made some mistakes on. If anyone has any more to add, insight, or corrections definitely go ahead and mention, hopefully we can make a fully comprehensive list.