Me, my group, bystanders, the victim

When an accident does take place, everyone wants to help. There is a sense of urgency because this is our friend. Stop, think, and plan before taking action. This process may need to be quick in a heads down situation with experienced rescuers or more deliberate when unpinning a boat without a paddler in it. You need to set priorities in any rescue and these priorities may surprise you:

Me - Ensure you don't add yourself as a rescue victim. Rescuing one person is always easier than multiple persons.
My Group - Keep a close eye on your fellow boaters. If you have novice boaters in your group, direct them to stay in a safe eddy. Alternatively, you can have them get out on the river bank and warn others from above. Novices may wish to help but many can't roll and will often swim compounding your problems.
Bystanders - This may be other parties or hikers on shore. You have no idea of what their skill levels are. They may be useful in reserve for pulling, getting help, etc. If you are a trip leader with a bunch of newbie's, think twice about abandoning your team to get involved in another group's rescue efforts if doing so jeopardizes your team (like running out of daylight for instance).
The Victim - Yes, the victim comes last. Once you are fairly confident that you can rescue the victim safely, proceed with the rescue effort.

Simple and fast to complex and slow

We have two other priorities and they sometimes conflict with each other. Most of the time, we prefer simple solutions over more complex ones. Complexity often goes hand in hand with danger. A great example is the Armstrong method (pulling on a tag line with lots of people) versus a Z-Drag (3:1 mechanical advantage system). The Z-Drag is far more complex and places a great deal of stress on ropes. The second goal is faster recoveries. This is far more important in a heads down pin than boat extraction. Rescuing a stranded swimmer in cold water needs to be done quickly as well to avoid hypothermia. We use the acronym RETHROG to prioritize our efforts in terms of safety.

RE - Reach Perhaps you can extend a paddle to the victim. This is fast and very safe. If you are in danger of falling in, simply drop the paddle.
TH - Throw This is where our trusty throw rope comes into play. Practice this skill often as it is the bread and butter of many rescues.
RO - Row A slight stretch of the imagination, in our case it means paddle in your boat to the victim. Set safety below as in many cases the rescuer will have to get out of their boat and let it float downstream.
Go - Go This is the most dangerous maneuver but may be necessary when you need a person to hold up the victim or maneuver them out of an entrapment.

You may be wondering why I said these priorities may occasionally be in conflict. Swimming to a victim is often the least complex method and at the same time has the highest risk factor. This is where experience and judgment play a vital role in evaluating your options. In a boat pin, time isn't as essential so don't risk a free swim if you don't have to.