I think one thing that's missing from a lot of shooters is variety. Peopel get bored of teh slew of black and brown hunks of metal all derived from teh same thing that you throw at them.
What comes to mind with a great shooter is Ratchet and Clank or Team Fortress 2. They have such a wide array of imagination, innovation, and even comedy with their weaposn that it's a refreshing feeling from what you normally see.
Another great addition to shooters is mobility. Games like Brink, Mirror's Edge, and Gotham City Imposters all allow players a freedom of movement that is hard to give up when they decide to play another game. While each of those games has their flaws, they have an underlyign freedom that can really grab players.
That's just to keep things fresh though. When you want true innovation, that's all about you. Innovation has to come from you. Whether you want to innovate story, gameplay, or design is soemthing you have to decide. Doing several is possible but can be a large undertaking. Ultimately, innovation is just blending an idea into the popular format. It's tough to get the perfect mix, but when you do, you can really make a change in the medium.