What are the likes and dislikes of the companions?

You can find the likes and dislikes of each companion on their respective page on the Fallout wikia.

Below you'll find some general guidelines and repeatable actions that affect companions' approval. Beside these general guidelines, companions like and dislike specific choices. For instance, Valentine likes giving Piper an interview, Cait likes keeping the Brew Buddy, and so on. You can find a list of specific choices people have noted on the characters' respective wiki pages. The lists on the wiki will likely continue to be updated with more specifics over time, so I would encourage you to look there as well.

Cait

Likes picking locks, doing certain chems, and generally mean and violent behavior. Cait's attitude toward chems can be permanently affected by a certain quest. Dislikes killing non-hostile targets, helping any main faction beside the Brotherhood, and avoiding fights.

Codsworth

Likes being lawful and helpful, loves crafting new mods. Dislikes being greedy or dishonest and irresponsible actions like chem addiction.

Curie

Likes supportive and selfless dialog and quest choices. Dislikes asking for extra money, stealing, unnecessary violence. Hates flirting with others.

Paladin Danse

Loves dedication to the Brotherhood and crafting mods. Likes entering power armor, helping settlers, and being reasonable. Dislikes ghouls, bribes, drugs, synths.

Deacon

Likes picking locks, hacking terminals, helping people, and nonviolent resolutions. Dislikes asking for more money and chems.

Dogmeat

As the wiki page puts it: "Dogmeat loves the Sole Survivor unconditionally, and thus is neither negatively nor positively influenced by their actions."

John Hancock

Loves defending the innocent and fast-traveling naked, apparently. Likes chems, hurting people who deserve it. Dislikes stealing, cruelty, being greedy.

Robert MacCready

Likes sarcasm, helping children or parents, and mercenary behavior (like asking for more money). Dislikes the Brotherhood and the Railroad, asking for too much money (last red option), and taking the moral high ground. Hates getting caught committing crimes.

Nick Valentine

Likes selfless and kind acts and hacking terminals. Dislikes threats, stealing, and murder.

Piper

Likes picking locks, helping innocents, and a mix of sarcasm and honesty. Dislikes stealing, lying, intimidation, greed, and the Institute.

Preston Garvey

Likes customizing weapons and helping others, especially settlers. Dislikes using the fatman, asking for money, satisfying an addiction. Hates stealing.

Strong

Likes helping others, being violent and aggressive, doing shady stuff. Disapproves of picking locks, hacking terminals, entering power armor, and persuading with charisma.

X6-88

Likes entering power armor, assisting the Institute, hacking, mods, and successfully demanding caps. Dislikes helping others, being naked, and using chems.