There were very few developed recurring characters in TOS or TNG; this changed with DS9, and was carried over, to a degree, to both Voyager and Enterprise. Continuity also exists in both of the latter series in the form of ongoing arcs that are revisited more than just once or twice, which is what tended to happen on TNG. A few key examples:
* The development of the romantic relationships between Tom and B'Elanna and Trip and T'Pol
* The Q, Borg, Species 8472, and Hirogen story arcs from Voyager, all of which were extended over the course of multiple episodes and seasons and were progressive, with each subsequent piece of each arc building on the previous installment
* The Archer vs. the Klingon Empire, Temporal Cold War, and Xindi story arcs from Enterprise, all of which again were progressively built and extended over the course of multiple episodes and/or seasons
You also have the recurring and progressive use of certain alien races from both series, which is much closer to the way things were handled on DS9 than the way things were handled on TOS and TNG.
Anyway, this is veering off topic, so I digress. DS9 was definitely the most consistent when it came to establishing and maintaining continuity, but there's not the huge discrepancy between it and the series that followed it that I think a lot of people might think there are.