So in terms of Star Trek, to me at least, it has 2 elements in every series. Cooperation of some sort, and a base story. Lets review:
TOS: Cooperation was between ethnicities. It did, after all, have crew members from many different cultures, many of which were suffering discrimination at the time. It had the first interracial kiss on camera, and its formula of having different ethnicities continued after it ended. Its story was about breaking out, into space. It showed that space IS interesting, and how sci fi can take you places you can only dream about
TNG: Cooperation was between factions. It focused on the many different races, and how the Federation interacted with them, and even helped support them. The fundamental ideals of the Federation were established, and how those ideals were viewed by the other races. Its story was of exploration and study. They showed different cultures, areas of space, technology etc.
DS9: Cooperation was also between factions, but in a different way. Where TNG had a backseat to many different factional conflicts, and focused on how the other races worked, DS9 was about how they work together in times of great need. It touched on racism as well, and how it was wrong. It was quite simply, a war story. It focused on how, even in the future, war is no only in existence, but how devastating it really is.
Voyager: (I liked Voyager :p) Cooperation was again the crew, but in more of a family or community way. It focused on how the crew interacted with a sole purpose, the purpose of getting home. Lost, deep in space with no help and little resources was the story. It mirrored some other already done sci fi shows, but kept the Star Trek theme and ideals.
Enterprise: Cooperation was the creation of order. The Federation was not created, Enterprise was about that creation. It focused on helping those that could help solidify the humans, as a race who can survive in the vastness of space. It dealt with time (Personally hated that) and how time is a fickle thing. One minute, all is well, the next, all hell breaks loose.
Heck, lets even through in the Movie: Cooperation was between human emotions. You have the hot head, randy, arrogant punk on one side. On the other, the calm, collected but unstable. Only by working together, could they succeed. Its story was about revenge, and how loss can drive even the best men to act like morons.
So whats next? If there is a new series, what would it be? Is there anything left?
My thoughts: Rogue. Its happened before, in ST3, Kirk went rogue, taking the Enterprise to look for Spock. A story about a rogue ship, and how its crew behaves knowing they are basically fugitives would be interesting to me. Cooperation would be between those that follow the Captain out of loyalty, but didn't want to leave, and those that share his thoughts, and would leave regardless. In my...personal thoughts, there is interaction between the Captain and the ship itself, but I'll leave that for another day.