Christian Creationism has its roots in the bible of course, and was largely used as an explanation for everything which could not be explained. The idea was almost universally accepted until the advent of modern scientific methods, and later the theory or evolution. For the next couple of hundred years creationism, particularly when adhering strictly to the word of the bible, was marginalized, and to some extent still is today. There has been a modern resurgence in evangelism however, and people are again starting to claim belief in creationism as stated exactly in the bible.
These days there are definitely two different camps regarding creationism within Christianity, namely the young earth creationists (also trading under intelligent design) and the general creationists. General creationism is basically the rest of Christianity, who believe that god created the universe, however either allows for and integrates evolution and science, or doesn't focus on it. Young Earth creationism on the other hand is the increasingly popular movement that believe that the Earth is only 5000 years old, and that mankind lived alongside the dinosaurs until they were killed by the flood of Noah.
For the most part, science and evolution have indefensibly smashed intelligent design and young earth creationism at every turn. So much so in fact that when the issue has gone to court several times, creationism often fails to turn up any defenders. The main reason being that a lot of what the fundamental Christian movement puts out is complete nonsense. This is more of a reflection of the people who are trying to further their own agendas than the ideal itself, however it does seem to discredit it somewhat.
They will often mix science with their own ideas and come up with entirely nonsensical arguments which they claim prove their point. For example Adam and Eve were the first humans and started the entire human race. This despite the fact that they would have had to procreate with their own children, and that the resulting mutations would have rendered the population extinct. And the rationale for this: mutations and diseases didn't exist back then (5000 years ago).
People do have the right to believe whatever they want of course, (see scientology for more details of an odd belief system). However surely something should have to stand up to basic scrutiny and at least not blatantly lie to people who don't know any better. Many movements of this kind are notorious for recruiting children and indoctrinating them into their beliefs by using all manner of methods, and many have been prosecuted on many occasions.
Creationism as an idea is an entirely different idea, as many of the fundamental ideas are still valid so long as you don't try to use the exact words of the bible. For example god could have started the process of evolution and the creation of the universe, and of course to something omnipotent the billions of years it took for between the big bang and mankind to evolve wouldn't seem that long.
The most modern science however is making even the idea of Christianity seem invalid to some extent. The fact that scientists have now proven the existence of other solar systems and planets has shown almost completely that there are certainly other life forms in the universe other than on Earth. There are billions of planets even within our own galaxy, and there are billions of other galaxies beyond our own. Thus surely a creator responsible for creating such a massive amount of races would have no personal investment in any of them.
Surely then if the idea of the Christian god is slowly being undermined by science, then the idea of a god at all is the next thing to follow. Well in actual fact this idea could be around a lot longer than any religion which personifies god in any way. A creator is still entirely possible, but is either immeasurably bigger than our own universe, or is more of a force of nature than a being that can interact with us in any way.