I'm assuming you're referring to genjutsu, since Amaterasu can burn a person even if they aren't making eye contact, and Susano'o can smash a person even if they aren't making eye contact.
The fight between Kabuto and Sasuke and Itachi in chapter 586 suggests that eye contact is needed to cast genjutsu, even if it's using an Eternal Mangekyou. During this fight, Sasuke had an Eternal Mangekyou, and Kabuto didn't seem terribly concerned.
Kabuto: "Since I shut off my vision, genjutsu won't work on me. I tell you again, you two have no chance of winning."
However, Izanami can be cast on a person even without direct eye contact. This is explained in chapter 587:
Sasuke: "So how? How can ocular jutsu work without eyesight?"
Itachi: "The Izanami is an ocular jutsu... that works with the physical senses of yourself and your opponents."
Izanami is very special though, so this probably isn't the norm. After all, Izanami is an incredibly powerful jutsu that blinds the Sharingan that is used to cast it. The general expectation seems to be that ocular jutsu requires eye contact, regardless of whether the Sharingan is regular, Mangekyou, or Eternal Mangekyou.
Though note also that Itachi can cast genjutsu from his finger. So even without Mangekyou, it doesn't need to be direct eye contact.