At this point, Eobard Thawne really needs no introduction. He is The Flash's ultimate nemesis, one whose role in the first season solidified him not just as the show's greatest villain to date but also one of the Arrowverse's as a whole. Despite being erased from existence by the end of season one, he's managed to return anyway time and again in one form or another, most recently leading the Legion of Doom in Legends of Tomorrow's second season and helping the Nazis of Earth-X attempt to conquer Earth-1 in the Crisis event.
Even when he loses, he always seems to have the upper hand anyway, his knowledge of the future in particular giving him an advantage that Barry and the team simply can't overcome. Thawne also has the benefit of being brought to life by two different actors, with Matt Letscher serving as the real face of Thawne and Tom Cavanagh serving as his Harrison Wells ruse, with both men delivering solid performances that compliment each other so well that they never overshadow one another.
He is the gold standard for villainy on The Flash, and even three and a half seasons in, his story is far from over, as we haven't even reached the fateful battle he'll have with Flash, the Green Arrow, and others in 2024 that sends the two speedsters back in time and ends with Nora Allen's death, let alone all the other battles the two are destined to have between now and then. When and how he'll show up next is part of the fun of his character, and The Flash simply wouldn't be what it is without him.