This is a complicated question and really depends upon the insurance laws of your state.
No-Fault States: if you live in a no-fault state then you could potentially leave your car in the street without insurance ONLY IF your car is parked in a legal zone and in a safe manner. What I mean by this is you do not want your parked car to be at risk for any liability in the case of an accident. For example, if you are parked on the street outside your house and it is within a couple of inches of the curb and no where near a fire hydrant, then if someone hits your car they will collect against their own insurance and you will not be liable if they sustain any severe physical injuries. However, if your car is in an illegal parking zone or you parked far from the curb, then the person who struck your auto might have cause for a liability suit against you. As a word of caution, just remember that you can get sued regardless of fault and you will have to defend the case until it is dismissed for lack of liability. This means you will still have to pay for an attorney, so it is better to have insurance.
Tort-State: you need insurance because they person who hits your parked car will sue you to reclaim collision damages.
Please note this is a very brief answer and there are other possible scenarios in both no-fault states and tort-states that can lead to you being sued for having your parked car in the street.
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No-Fault States: if you live in a no-fault state then you could potentially leave your car in the street without insurance ONLY IF your car is parked in a legal zone and in a safe manner. What I mean by this is you do not want your parked car to be at risk for any liability in the case of an accident. For example, if you are parked on the street outside your house and it is within a couple of inches of the curb and no where near a fire hydrant, then if someone hits your car they will collect against their own insurance and you will not be liable if they sustain any severe physical injuries. However, if your car is in an illegal parking zone or you parked far from the curb, then the person who struck your auto might have cause for a liability suit against you. As a word of caution, just remember that you can get sued regardless of fault and you will have to defend the case until it is dismissed for lack of liability. This means you will still have to pay for an attorney, so it is better to have insurance.
Tort-State: you need insurance because they person who hits your parked car will sue you to reclaim collision damages.
Please note this is a very brief answer and there are other possible scenarios in both no-fault states and tort-states that can lead to you being sued for having your parked car in the street.
I hope this helps.