The Listed Trilogies:
Star Wars Prequel Trilogy - technically, this IS the next Star Wars but I am guessing your looking for opinions on what will be the next film series still big in 30, 40, and 50 & beyond years. Honestly, I don't think whatever it is will come along until Star Wars is officially done.
The Matrix Trilogy - a little bit ahead of it's time perhaps and maybe released too closely together. If it had been released at a time when Star Wars was officially dead and perhaps over 5-7 years instead of 4 with 2 in the same year then maybe it is the next Star Wars... if released in 2035.
Halo Trilogy - Star Wars introduced the world to the possibilities of what could be going on out in space. This movie would just be expanding upon that, it's not breaking any new ground. What it does have going for it is that the next Star Wars might not be a movie at all, rather just a video game. Of course there are around a dozen or so other titles that are vying for that spot.
Avatar - it really did break some good 'new ground' but it did it with technology as opposed to story and settings which, ultimately, are what a movie needs most.
The Lord of the Rings - definitely a memorable trilogy that will surely be around for many years, if it's not overplayed. It's not the next Star Wars though, simply because - Star Wars was not finished.
Harry Potter - I still haven't seen any of these movies and the fact that I have no interest in doing so should probably be enough to know... it's not the next Star Wars because if it were I'd be interested in seeing it.
Twilight Saga - I have less interest in this than I do in Harry Potter.
Iron Man, Sam Raimi's Spider-Man Trilogy, X-Men, Nolan's Batman Trilogy, The whole Marvel Cinematic Universe, Green Lantern - These all cross each other out. The mass influx of comic book/superhero movies will prevent any of them from being the next great trilogy.
Pirates of the Caribbean - No.
So what do I think is the next Star Wars? To my dismay, it may be a little thing called World of Warcraft - and it's not a movie. Thankfully, there is still a chance that, like The Matrix, it to is a bit ahead of it's time. Could it be the the sole purpose of The Matrix coming into existence was/is to keep World of Warcraft down? This world may never know.