This is a large topic of discussion and the impetus behind many, many stories in the DC universe (I don’t follow Marvel; maybe there too). In DC, the governments of the world tend to build up their own superpowered forces by genetic recombination, brainwashing, blackmail, cloning, plain old patriotism, and other tactics. Captain Atom is a good example of a superhero sometimes torn between his duty to the Justice League and his duty to his country.
The Suicide Squad (aka Task Force X) is one such government agency. Project Cadmus is another, though sometimes they have other goals. Amanda Waller is my favorite government anti-hero who works to offset the power of the superheroes, though she is not superpowered herself. Even STAR Labs eventually works to further government interests in opposition to the Justice League, after Professor Hamilton becomes disillusioned with Superman’s rhetoric. There’s also a large story arc involving Lex Luthor as President for a bit (he’s not usually superpowered, but sometimes is, especially when Brainiac is involved).
You might be interested in the comic Red Son, which is a depiction of the person Superman might have been if his capsule had landed in the USSR.
So to answer your question – there are a lot of political and legal ramifications of superpowers, and if you’re interested in this, check out a bunch of comics, because a lot of cool scenarios have already been imagined. A great way to take in one of these, involving a good deal of what I mentioned above, is to watch Bruce Timm’s Justice League Unlimited (Not Justice League – which, though also a great series, is not political. JLU is the direct sequel to JL).