1. Isn't afraid of being slow, talky, and philosophical (Sorry J.J.). TNG had many excellent episodes specifically because it was willing to risk being "boring", while DS9 evolved Trek into the homogeneous "action" formula that has dominated Voyager, most of Enterprise, and the recent movies.
2. Is a force for idealism. The captains of Star Trek are paragons of humanity, and are supposed to find the high ground when tackling murky issues. The original series featured the first on-screen interracial kiss. TNG dove into many thorny ethical issues. While TNG took a hard stance against torture, Enterprise portrayed it as a useful tool.
3. Boldy goes to new places. Star Trek (2009) did nothing new geographically, but at least it went off the reservation by destroying a storied and beloved Trek locale. Not everyone liked that, but at least it was daring. Into Darkness (2013) aped Khan badly, completely missing out on what made the original character and movie special. In general, the Trek movie franchise has been chasing Khan for too long, and needs to focus on other aspects of Trek.
4. Is smart about technology, and self consistent. Nerds pay attention to this stuff. Khan beaming directly from Earth to the Klingon homeworld functionally obliterated the vastness of space in the rebooted Trek universe. Trek doesn't need to blow previously imagined sci-fi tech out of all proportion to be interesting. It's strength, historically, has been inventing new technologies and examining their impact on humans. Is there anything in the new Trek movies that, in a few decades, we're going to be saying, "Hey, Trek predicted this!".
5. Doesn't solve everything by modifying the deflector dish. (Corollary to 4) Voyager, I'm looking at you. All of the series occasionally penned "tech" into their scripts to lazily magic their way out of situations. At some point this became standard practice and as much a part of the formula as always having at least a few minutes of "action trek", no matter how inappropriate it was to the episode. This is a crutch that should be used as sparingly as possible.
6. Features interesting, well-developed alien cultures. The original series may have debuted the Klingons, but it was TNG that fleshed them out into a living, breathing culture. TNG debuted the Cardassians and Bajorans, but DS9 benefited greatly from exploring the cultures of both these races. The formula of Voyager forced a return to shallow portrayals of "species of the week", and the show suffered greatly as a result.