If your cleats are misaligned, the forces involved in standing will magnify the torque on your knees. Same with weakness in the hip stabilizers that don't necessarily get a lot of use when you're in the saddle. Something to think about.
Related to what Eden said about reach, try to keep your weight over your bottom bracket. That'll both help keep your weight over the rear wheel (to give you traction so the tire doesn't slip) and help you fully extend your knees. Don't be shy about fully extending your legs.
To me, climbing and sprinting out of the saddle pretty much feels like doing step-ups. Which, again, use a lot of hip stabilizer muscle to keep the knees in alignment.
ETA: the OP asked about tight turns, too. It's not really one of my strengths
but the general principle is to look where you want to go. Scan the ground for obstacles and loose stuff, then pick your eyes up and look over your shoulder. Looking at the ground is a sure way to wind up on it. Unlike a high-speed turn, don't lean into the turn, but keep your weight centered or even slightly to the outside. And commit, don't hesitate, once you're in the turn.
Last edited by OakLeaf; 11-24-2009 at 08:05 AM.
Speed comes from what you put behind you. - Judi Ketteler