You are a biker and you hit a pedestrian
I've never done that, but in many places you are legally required to stop and render assistance. Also, it's the non-a**hole thing to do.
You are a biker and you hit a biker
Again, stop, make sure the other person isn't hurt and doesn't have any mechanical trouble that'll stop them from riding.
If there is an injury or either party thinks it necessary, exchange contact info and/or wait for a responding officer.
You are a biker and you hit an inanimate object
If it's someone else's property, like a car or a mailbox, and there's damage, leave a note with your contact info.
As Johannes points out, in some jurisdictions, a note might not be enough. You might be assumed to have fled if you don't make an attempt to contact the owner or file a report with the police.
You are a pedestrian and a biker hits you
In many places, the cyclist is probably at fault since there are no highways for bikes where the pedestrian isn't assumed to have right-of-way.
Ask for contact info, and offer assistance if the cyclist is injured. If the cyclist leaves the scene without stopping, remember details (what the cyclist looked like and was wearing, their frame color and design), and file a police report.
You are driving a car and a biker hits you
Same as in a car/car collision. Stop, render assistance and give a report to any responding officer if either party is injured or thinks a report is necessary.
You are an inanimate object and a biker hits you
You are a biker and you fall over in the middle of the road and everyone laughs at you
I've done this.
Pick yourself up, and declare that you meant to do it. Ride off pouting. Realize your wheel is now out of true. Stop. True it enough with the wrong size nipple wrench until it stop scraping against the fenders. Ride off pouting again.