Realistically there wasn't much of a long term impact.

Once it became too costly for the Barbary States to continue preying on US merchant ships they turned to other prey which they had long found appealing such as the Italian states or Spanish ships. They were business first and foremost, seeking ships from nations either too weak to respond at all, or willing to bribe them off, once the US had shown like Britain that they were willing and bale to make it too costly they in general stopped, only the chaos of the late Napoleonic wars and 1812 led to the resurgence then put down in the 2nd war.

The Barbary states continued their piracy for several more years until a combined fleet led by Britain put a stop to it for good, and several decades later you see the start of both the French and Italian colonial adventures in North Africa turning much of the coast into colonial possessions.

For the US it did not spark any sort of surge of foreign commitments either before or after 1812. It was a limited action run with the smallest possible budget and manpower to ensure the continuance of free trade. And while heroes did emerge from it in the popular consciousness and the esteem of the Navy improved at home and abroad thanks to the likes of men like Decatur (his burning of the Philadelphia was remarked upon as the most bold and daring act of the age by no less then Nelson himself).

But 1812 did much more to establish the USN as a credible service, and for most of a century the US and the Navy still had minimal foreign postings, particularly in Europe. Only with the warming of relations with Great Britain, and the acquisition of colonial possessions did the USN become the global force it is today.

It did however continue the trend of the US to fight for freedom of the seas and freedom of commerce, the Quasi War, the Barbary actions, and 1812 all served in large part to confirm this as a major principle of foreign policy that the US was willing to use her Navy to enforce.