While Rozwel covered some basics in their answer, there's some other things to consider
Is the liability disputed?
I had a woman hit me (construction zone with poorly delineated lanes) and she claimed I hit her. In this case, I had no choice but to file a claim against my insurance (her insurance tried to claim against mine but was not successful). I had to pay a deductible and that was it. Remember, if they claim you're at fault, they will file against your insurance. In this case, it's moot if you file, because your insurance will make you jump through hoops anyways (even if you leave your car unrepaired). If their claim against you is successful, there's a good chance your rates will go up. In my case, blame could not be determined reasonably so neither side got the other to pay damages.
By contrast, I had a woman back into my car in a parking lot. Severely damaged the hood and the front bumper. She admitted liability and I filed directly with her insurance. In this case, I had no deductible and they paid for my rental. Was surprisingly painless. If they admit liability, your rates won't change because you never file with your insurance.
If the other side has no insurance, what will happen when you file is that your insurance company will sue the other side to recover damages (most insurance companies arbitrate disputes with one another).
Your damages are almost certainly more than your deductible
Unless we're talking a small dent, most damages mean your vehicle will have the damaged parts disassembled, repaired/replaced and then painted to match the vehicle. Rarely will that be below $1000. I had a side panel and mirror damaged. Was about $2500 in repairs.
Can you be without your vehicle for some time?
If you drive to work and don't have loss-of-use coverage (where the insurance company gives you a rental), you might be without a vehicle for several days. That might cost you more than your deductible would alone.
The other side will probably sue your insurance, not you
Unless you're pretty wealthy, the other side wants a payday. Your insurance company has much deeper pockets and they make a much more tempting target (see your local attorney billboard if you need proof "We take on the big insurance companies!"). Even if they do sue you directly, your insurance company may be obliged to defend you in most circumstances regarding your insured vehicle. Whether or not your insurance requires you to have filed a claim will have to be answered by your insurance company. I'd ask your insurance representative about this type of circumstance and how they handle it.