Use your companion as a scout/decoy/human shield.
Command your decoy by clicking/selecting them and pointing to where you want them to go. "Strong, go forth into that explosion to make sure the enemies are dead!"
Command your companion to enter your power armor! You can take it with you everywhere you go, and they won't use up any Fusion Cores while in it.
WARNING: Your suit may get damaged while your companion is wearing it, and you can't put it back on until it's repaired.
When you obtain one companion's perk, it'll stay activated even if they're not with you.
When you achieve Garvey's maximum Affinity, you'll permanently get his perks, even if you don't use him as a companion later.
And of course, dress your companions to impress.
Yep, Codsworth is wearing a bowler hat. As he should be!