Below, you will find information on each companions general likes and dislikes. I have also included their respective companion perks, in case this is a deciding factor on which companions a particular user wishes to focus on a relationship with.
A majority of the information has been summarised from the companions respective Fallout Wiki page. A lot of it is self-explanatory. A companions perspective on chems will dictate their feelings towards giving chems to Mama Murphy, and convincing her to get off them.
In most cases, a companion approving or disapproving of a faction or general race (for example, favoring The Minutemen, or disapproving of Synths) will effect their corresponding reaction to dialogue, actions and interactions with members of the respective faction or general class.
In most cases, a companion approving of being helpful will favor charitable actions, while a companion disapproving of charitable actions will approve of greedy actions. For example, charitable companions do not like it when you ask for a reward.
For more information, check each companions linked page, under "Effects of player's actions".
Cait
Full approval grants the Trigger Rush perk, giving the player an increase in action point regeneration, when the player is below 25% health.
Approval
Picking locks or stealing.
Chems, before her personal quest, and addictol, after her personal quest.
Alcohol, before her personal quest.
Violent behaviour.
Mean or threatening dialogue.
Being naked.
Asking for rewards for helping others.
Choosing not to join the Brotherhood of Steel
Stopping the Institute.
Destroying the Railroad.
Disapproval
Chems, after her personal quest.
Dialogue that avoids fighting.
Helping people.
The Brotherhood of Steel.
Cannibalism.
Killing non-hostile NPCs.
Flirting with other characters, once you are in a romance with her.
Telling Miss Edna that children need love, in Diamond City.
Selling Billy to Bullet.
Codsworth
Full approval grants the Robot Sympathy perk, giving the player a bonus of +10 energy resistance, against robots.
Approval
Responsible and lawful acts.
Helping others.
Family-orientated dialogue.
Prevention of death.
Crafting modifications.
Disapproval
Asking for money for helping others.
Dishonest dialogue.
Chems.
Accepting the order to hunt Paladin Danse.
Stealing.
Murder.
Curie
Full approval grants the Combat Medic perk, which allows the player to heal 100 hit points once a day, if below 10% health.
Approval
Helping others.
Dialogue favoring peace, reason or compassion.
Dialogue favoring robotics.
The Brotherhood of Steel.
Asking for a reward for delivering the pristine Deathclaw egg.
Synths.
Killing Gunner leaders.
The Railroad.
Sparing Dance during the quest Blind Betrayal.
Disapproval
Asking for a reward for most quests.
Returning the pristine Deathclaw egg to its nest.
Violence against NPCs, other then ghouls and super mutants.
Dialogue favoring violence or aggression.
Dishonest behaviour.
The Institute.
Killing a neutral Mister Gutsy / Mister Handy.
The town of Covenant.
Becoming addicted to chems.
Danse
Full approval grants the Know Your Enemy perk, which gives the player a bonus of +20% damage, against ghouls, super mutants and synths.
Approval
Power armor.
Vertibirds.
The Minutemen.
Dialogue favoring reason.
Helping others.
Being spared, during the quest Blind Betrayal.
The Brotherhood of Steel.
Crafting weapon, armor or power armor upgrades.
Disapproval
Super mutants.
Ghouls.
Synths.
Bribing.
Chems.
Cannibalism.
Dialogue regarding synths.
Attacking non-hostile NPCs.
Building artillery for the Minutemen.
Picking the locks of owned containers.
Flirting with other characters, once you are in a romance with him.
Deacon
Full approval grants the Cloak & Dagger perk, which gives the player a bonus +40% to the duration of Stealth Boys, and a bonus +20% damage to sneak attacks.
Approval
Lockpicking.
Hacking.
Helping people.
Resolving conflict through passive means.
Synths.
The Railroad.
Disapproval
Asking for rewards for helping people.
Attacking non-hostile NPCs.
Chems.
Cannibalism.
Covenant.
The Brotherhood of Steel.
Dog(meat)
Dogmeat does not gain approval, and will love you, no matter what. As a result, there is no perk associated with gaining Dogmeat's approval. However, Dogmeat will benefit from the Attack Dog perk, and does not count as a companion for the purposes of the Lone Wanderer perk.
John Hancock
Full approval grants the Isodoped perk, which gives the player a bonus +20% to the fill rate of the critical meter, provided the player's rads are at 250 or higher.
Approval
Chems.
Harmful or cruel action towards those that deserve it.
Helping or defending the innocent.
The Minutemen.
The Railroad.
Naked fast-traveling.
Disapproval
Stealing.
Greed.
Cruelty towards those that do not deserve it.
The Brotherhood of Steel.
The Institute.
Convincing the Vault-Tec rep to leave Goodneighbour.
Flirting with others while in a relationship.
Nick Valentine
Full approval grants the Close to Metal perk, which gives the player an extra attempt when hacking, and reduces the lockout time for failing a terminal by 50%.
Approval
Helping others.
Hacking.
Resolving conflicts peacefully.
Dialogue favoring synths.
The Railroad.
Disapproval
Dialogue favoring aggression or threatening behavior.
Stealing.
Murder.
The Brotherhood of Steel.
Cannibalism.
Greed.
Picking an owned lock.
Covenant.
Piper Wright
Full approval grants the Gift of Gab perk, which gives the player doubled experience for finding locations, persuading people, and lock-picking.
Approval:
Helping the innocent.
Lockpicking non-owned locks.
The Minutemen.
Resolving conflicts peacefully.
The Railroad.
Telling the truth.
Disapproval:
Stealing.
Lying.
Lockpicking owned locks.
Covenant.
The Institute.
Dialogue favoring aggression or threatening behavior.
Chems.
Murder.
Asking for rewards.
The Brotherhood of Steel.
Cannibalism.
Flirting, if the player is in a relationship with her.
Preston Garvey
Full approval grants the United We Stand perk, which gives the player a bonus +20% damage, and increases damage resistance by 20, when facing 3 or more enemies at one.
Approval
Helping the innocent.
Building weapon modifications.
Being honest.
The Minutemen.
The Railroad.
Disapproval
Using the Fat Man.
The Brotherhood of Steel.
Covenant.
Asking for rewards.
Chems.
Cannibalism.
The Institute.
Destroying the Institute without issuing an evacuation order.
Stealing.
Robert MacCready
Full approval grants the Killshot perk, which gives the player a bonus +20% chance to perform a head shot in V.A.T.S.
Approval
Asking for rewards.
Sarcasm.
The Minutemen.
Criminal action.
Helping children or parents.
General mercenary behavior.
Disapproval
Taking the moral high ground.
The Brotherhood of Steel.
The Railroad.
Helping others.
Asking for too much money (the red option, when asking for rewards).
Unprovoked violence.
Being caught during an illegal act.
Strong
Full approval grants the Berserk perk, which gives the player a bonus +20% to melee damage, if they are below 25% health.
Approval
Helping others.
Taking the aggressive path over the peaceful path.
Taking less-reputable quests.
Cannibalism
Stealing useful items
Disapproval
Lockpicking.
Hacking.
Power armor.
Using charisma-check dialogue.
Chems.
Taking reputable quests.
The Brotherhood of Steel.
X6-88
Full approval grants the Shield Harmonics perk, which gives the player a bonus +20% to energy resistance.
Approval
Power armor.
The Institute.
Hacking.
Creating weapon or armor modifications.
Asking for more rewards.
Disapproval
Helping others.
Being naked.
Vertibirds.
Chems.