No, deductibles are not due every time you are in an accident. You have to pay out a deductible though every time you use one of your coverages that have a deductible associated with it. Typically this is your physical damage coverages of Collision and Comprehensive but other coverages you have, such as PIP, you may choose to have a deductible with to save money on your auto insurance premium.
Let's look at the situations you described and if you would owe a deductible:
#1 - If you crashed your own car than you would usually need to use your Collision coverage to repair your vehicle and thus the deductible amount associated with your Collision coverage would be due.
If you crashed your own car, but it was caused by another driver, you would file it under the at-fault driver's Property Damage Liability and not pay a deductible.
#2 - If you crashed your friend's car than their insurance would be primary and they would owe the deductible amount for their Collision coverage. You however as the driver that was at fault in the accident would likely be looked to by the car owner to pay their deductible for them. And to be a good friend you would want to pay the deductible or your friend may take you to court to sue you for the deductible amount they are out due to your crashing their car.
If you crashed your friend's car, but it was caused by another driver, you would file it under the at-fault driver's Property Damage Liability and not pay a deductible.
[Let CarInsurance.com help you find affordable auto insurance now.] #3 - If you injured someone, either a pedestrian or a driver or passenger in a car that you hit than normally this would go through your Bodily Injury Liability coverage. With your Liability coverages, both Bodily Injury Liability (BI) and Property Damage Liability (PD), there is not a deductible to be paid by you or the party making the claim against your car insurance coverage. Your BI coverage would cover the injuries you caused to others and PD would pay for the person's car that you hit.
So deductibles are not due every time a claim is made. It depends upon if you are using a coverage which has a deductible amount associated with it or not. You can read through your car insurance policy and coverages to see when deductibles are due according to your policy.
As you know the deductible is the amount of money you have to pay before your insurance company begins paying the rest. Your insurance premium will normally go up when you choose to have a lower deductible amount. In contrast if you raise your deductible amount your rates should go down.
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If you choose to pay for smaller items yourself, such as little dings and bumps, and claim expensive damage so your insurance company pays, minus your deductible it should save your money on your car insurance premium. This is because you would be paying for smaller damages that cost less to repair than your higher deductible amount.
Instead your financial situation may call for you to lower your deductible so you know that you can afford the deductible amount if your car is damaged and you need to use your Physical Damage coverages. You do not want your deductible so high that you cannot afford to pay out that amount to get your car fixed because you cannot come up with this money. Your rates may be higher but it may be worth it for your personal situation. | 
