This would probably work better as a TV series like the Twilight Zone or The Outer Limits, with perhaps the longer stories spread between a few episodes. I would call it "Larry Niven's Known Universe."
Obviously, this would be a series of standalone episodes based on the stories of Larry Niven, specifically the ones set in what he calls his "Known Universe." Many of them are short stories perfectly suited to one-hour episodes, but some are longer novels (Ringworld for one, World of Ptaavs for another) which would require a miniseries. They all share the same planets, some with names like Jinx and We Made It, although they are generally restricted to one locale per story, and some share characters, although the Known Universe stories encompass centuries, if not millenia.
Such a broad scope may not work well, however. Star Trek: Deep Space Nine has shown that civilian storylines do not hold much interest for sci-fi fans. The best DS9 stories are considered to be the ones involving the Dominion War, which, of course, was a special effects tour de force. So perhaps the Known Universe should be pared down to the subset of "Tales from the Man-Kzin War." I think tales of Man fighting 500lb tiger-like aliens who leap first and think later (if at all) could be quite gripping, from first contact through several centuries of alternating peace and war. The action occurs in several planetary systems and therefore not every human would be involved in every episode, but when a human actor is not central in a particular episode he/she could probably find a spot in a "ratcat" suit.
The thought of seeing Niven's stories on screen positively warms my liver! Any comments?