Is there evidence that supports the "theory" of (fundamentalist) creationism? Because creation theory in general does not have specified boundaries, just about anything could be considered "evidence" for or against it. A legitimate scientific theory must make specific, testable predictions and be falsifiable in specific, predictable ways. Evolution fulfills both of these conditions and many more, but creationists are unable or unwilling to make their theory fulfill them.
God of the Gaps "Evidence" for Creationism
Most of the creationists' evidence is of the god-of-the-gaps nature, meaning that creationists try to poke holes in science and then stuff their God into them. This is essentially an argument from ignorance: "Since we don't know how this happened, it must mean God did it." There are and probably always will be gaps in our knowledge in every scientific field, including of course biology and evolutionary theory. So there are plenty of gaps for creationists use for their arguments — but this is in no way a legitimate scientific objection.
Ignorance is never an argument and cannot be considered evidence in any meaningful sense. The mere fact that we cannot explain something is not a valid justification to rely upon something else, even more mysterious, as an "explanation." Such a tactic is also risky here because, as science progresses the "gaps" in scientific explanation grow smaller. The theist who uses this to rationalize their beliefs may find that, at some point, there simply isn't enough room for their god anymore.
This "god of the gaps" is sometimes also called deus ex machina ("god out of the machine"), a term used in classical drama and theater. In a play when the plot reaches some important point where the author cannot find a natural resolution, a mechanistic apparatus will lower a god down onto the stage for a supernatural resolution. This is seen as a cheat or contrivance of the author who is stuck due to his own lack of imagination or foresight.
Complexity & Design as Evidence for Creationism
There are also some positive forms of evidence/arguments cited by creationists. Two currently popular ones are "Intelligent Design" and "Irreducible Complexity." Both focus on the apparent complexity of aspects of nature, insisting that such complexity could only arise through supernatural action. Both also amount to little more than a restatement of the God of the Gaps argument.
Irreducible complexity is the claim that some basic biological structure or system is so complex that it's not possible for it to have developed through natural processes; therefore, it must be the product of some sort of "special creation." This position is flawed in numerous ways, not the least of which is that proponents cannot prove that some structure or system could not have arisen naturally — and proving the something is impossible is more difficult than proving that it is possible. Advocates of irreducible complexity are essentially making an argument from ignorance: "I can't understand how these things could arise from natural processes, therefore they must not have."
Intelligent Design is usually based in part on arguments from irreducible complexity but also other arguments, all of which similarly flawed: the claim is made that some system could not possibly have arisen naturally (not just biological, but also physical — like perhaps the basic structure of the universe itself) and, therefore, it must have been designed by some Designer.
In general, these arguments aren't particularly meaningful here since none of them exclusively support fundamentalist creationism. Even if you accepted both of these concepts, you could still argue that the deity of your choice was guiding evolution such that the characteristics we see came to be. So, even if their flaws are ignored these arguments can at best be considered evidence for a general creationism as opposed to biblical creationism, and therefore do nothing to alleviate the tension between the latter and evolution.
Ridiculous Evidence for Creationism
As bad as the above "evidence" may be, it represents the best that creationists have been able to offer. There are in fact far worse sorts of evidence which we sometimes see creationists offer — evidence that is either so preposterous as to be almost unmentionable or demonstrably false. These include claims such as that Noah's ark has been found, flood geology, invalid dating techniques, or human bones or tracks found with dinosaur bones or tracks.
All these claims are unsupported and/or have been debunked many times, yet they persist despite the best attempts of reason and evidence to stamp them out. Few serious, intelligent creationists put forward these types of arguments. Most creationist "evidence" consists of an effort to refute evolution as if doing so would render their "theory" somehow more believable, a false dichotomy at best.
Disproving Evolution as Evidence for Creationism
Rather than finding independent, scientific evidence that points to the truth of creationism, most creationists are concerned primarily with trying to disprove evolution. What they don't recognize is that even if they could demonstrate that evolutionary theory were 100% wrong as an explanation for the data we have, "god did it" and creationism would not therefore be automatically more valid, reasonable, or scientific. Saying "god did it" wouldn't be treated as more likely true than "fairies did it."
Creationism will not and cannot be treated as a legitimate alternative unless and until creationists demonstrate the their proposed mechanism — god — actually exists. Because creationists tend to treat the existence of their god as obvious, they are likely to also assume that creationism would automatically take evolution's place if they could just "dethrone" it. This, however, merely demonstrates how little they really understand about science and the scientific method. What they find reasonable or obvious doesn't matter in science; all that matters is what one can prove or support through the evidence.