Warning: This article contains spoilers for Titans season 2, episode 1.
The demonic Trigon was defeated, and possibly even killed, in the Trigon emerging and beginning the process of corrupting the Titans to his cause.
The season 2 premiere, "Trigon," finally explained how this worked. Trigon appears to feast on negative emotions, and as such he needed Rachel's heart to be broken in order to manifest on Earth. To that end, he had Dick Grayson apparently kill Beast Boy, forcing Rachel to watch her mentor murder her best friend. Naturally, the experience left Rachel traumatized, and Trigon used her heartbreak to draw her power to the surface. That done, he could step out of the haunted house's door, and unleash his power on the world.
Fortunately, Trigon had underestimated Beast Boy, who had survived. He was able to break Trigon's influence over Rachel, and she turned her power on her own father. The Titans season 2 premiere was unclear quite what happened, but it looked as though Rachel was able to force Trigon back into his home dimension. Although it seemed to be a painful experience, it's reasonable to assume Trigon isn't dead.
It's clear that Rachel's powers are strongly tied to her emotions; Trigon was able to take advantage of her negative emotions to enter the world, but she was able to banish him with positive emotions. Rachel was described as a sort of "living doorway" to Trigon's plane of existence in Titans season 2, episode 3, and that essentially means that Trigon could return at any time. So long as Rachel is happy, and around her friends, Trigon has no access; but all she needs is a single moment of despair, and he can begin to influence the world again. Fortunately for the Titans, Trigon no longer has any servants on Earth; he made the mistake of killing Raven's mother, confident that he'd already triumphed.
In theory, then, it's quite possible that Trigon will return. In practice, it's more reasonable to assume Titans will consider the threat of Trigon to be resolved. The Trigon plot dominated the entire first season, and the show appears to be in something of a hurry to move on to other villains, such as Deathstroke. Trigon may not be dead, but it's unlikely viewers will see him again.