Personally, I don't want to re-hash the stuff that's gone on before. I want a new series, set after the end of Voyager/Nemesis. The galaxy's a political mess at this point, with Cardassia being decimated, the Romulan Senate assassinated in a coup that fell apart, the Federation still rebuilding its fleet after the Borg disaster and Dominion War, etc.
My personal choice?
Star Trek: Elite Force. C'mon, you know it would work...
The two main ST series were products of their times. TOS was made at the heart of Cold War tensions, during a period when social and political traditions were being questioned & challenged, while smaller nations waged their own wars (sometimes with help of the Superpowers).
TNG was made when the Cold War was ending, many of the old social quandries were being relegated to history and people were re-examining the way they interact with one another, while smaller nations waged their own wars (using stockpiles bought on the Black Market from the Superpowers, if not being helped by former members of said Superpowers).
Now, we're in a world with one Superpower, new social and political questions are taking to the forefront, and there's the everpresent issue of national and social violence throughout the world (focusing more and more on Black Market stockpiles and funding from independantly wealthy sources, rather than any particular powerful nation).
I think an EF series would fit the feel of ST at this moment. Exploration is still a fundamental part of the feeling, but there's also the need to keep dangerous situations from getting out of hand while the various forces of the ST universe lose stability and try to rebuild. The EF group might be helping explore a world in disputed territory, guarding supplies being shipped to a world in need, or acting in a military capacity to end a violent situation. There's plenty of room for personal interaction, hard political and social questions, and action, all at once.