It's late, and perhaps in the coming days I can add citations in a (probably hopeless) attempt to match the excellent research of at the top of the node. Nor am I a lawyer; but even lay-persons have a duty to understand the law as best we can, even arcane complexities of International Law. So here goes:
The way I read the history books, the original no-fly zones, including the infamous helicopter exception, were negotiated in a tent in the desert by Stormin' Norman and the other coalition and Iraqi generals. This was simply a multi-lateral agreement between warring parties, to which the UN wasn't formally a party. Granted, there's no explicit granting of authority in the UN charter or and of resolutions for the Iraqi no-fly zones, but neither do they or any other aspect of International Law (which long predates the UN!) appear to prohibit parties from entering into, and enforcing, bi- or multi-lateral agreements. In short, my understanding is that Saddam, not the UN, agreed to the no-fly zones in order to stop the war and stay in power. Later UN resolutions such as 686 - 688 certainly don't appear to explicitly authorize no-fly zones. Not being a lawyer myself, I can only assert my strong suspicion that US lawyers were smart enough to craft those UN resolutions so that they didn't render the earlier, multilateral agreement entirely void...in which case the legal argument would be that in the earlier, non-UN cease-fire agreement, Iraq had exercised its prerogative to define its "sovereignty" in such a way as to accept overflights, so subsequent US resolutions requiring Iraqi sovereignty be respected are not violated by the overflights per se.
As to the bombing, in 1993, of targets in and around Baghdad, in response to the alleged plot to kill George Bush: clearly this bombing exceeds the definition of sovereignty that allows for no-fly zones. Here an argument would be self-defense of US sovereignty, which includes the person of the commander in chief, but only if you believe the plot was real. Another argument would be that Iraq had already violated the cease-fire, by directing surface-to-air targeting radar at overflight aircraft prior to 1993, in a ham-handed attempt to re-claim the sovereignty he'd given up in 1991 in order to stay in power. Under this second argument, the cease-fire was now void, and ongoing enforcement of the no-fly zones, and other operations besides, would be justified under Resolution 678 (1990), which authorized member states to apply "all necessary means".
And of course all these lovely legal arguments got trashed by the time the DOD and State Dept spokesmonkeys got filtered through the pressmonkeys to the public (monkeys, one and all!), resulting in soundbytes such as "The UN-mandated no-fly zones"...but the various statements to the press and the public do not in and of themselves have legal force.
One of the problems with international law is, as far as I know there is as yet no single, sovereign authority for deciding cases of international law. Traditionally, before the UN, I suppose treaty disputes would be resolved by diplomats, essentially a political exercise, or by arbitrators, for example in commercial disputes. These arbitrators based their authority on their reputations for independence and fairness. War Crimes would be adjudicated by tribunals whose jurisdiction and authority was limited to a particular conflict. Now we have the International Criminal Court, or ICC, which is designed to be the sovereign authority. However, former President Clinton declined to sign the treaty that would have establish the ICC's authority over the US military, and even if he had, the Senate probably would not have ratified it.
So that's my take on legal points. As to the wisdom, or lack thereof, of even bothering with no-fly zones, I refer you to my The United States is Already At War With Iraq.