One of the first questions I ask, before even getting into an Internet debate at all, is "Does the claim that I'm about to refute meet its own standard?" Why? Because any claim that doesn't meet its own standard is false, by its own definition! Such a claim is called a self-refuting or self-defeating statement. Below are just several examples, and I don't know about you, the reader, but I can spot their own admissions of self-defeat just by asking that question, starting, of course, with the obvious.
1. "There is no truth": If this is the case, if there is really no truth, then this very claim cannot be true either! This admission of self-defeat, however, doesn't stop atheists from using it. I've encountered it on the Internet all too often, and more than once it's used by people who claim to be beacons of reason and logic, as atheists often claim to be. Anyone who claims to be a beacon of reason only to make a claim like this one is not only contradicting his own claim in the debate but also contradicting his claims to reasonability in the process.
2. "All truth is scientific": Is this claim scientific in nature, or is it a philosophical assertion? Can one test this claim using the scientific method? Look at a written or printed copy of this claim under a microscope to see if you can find hard proof that the claim itself is true hiding somewhere in the pixels that make up the hard copy of the claim? No. It's a philosophical claim by nature. It's false, therefore, even by its own standard!
Moreover, even science itself hinges on unprovable assumptions, as William Lane Craig alluded to in a debate with an atheist back in 1998. Can one prove Einstein's general theory of relativity using the scientific method? No. We have to simply assume that the general theory of relativity is true in order to conduct physics experiments. Since science also depends largely on mathematical truths — again, can we prove math using science? No we can't. We have to simply assume that, for example, F=(Gm1m2)/d^2 in order to calculate what kind of gravity an object has, or that water consists of 2 parts hydrogen and one part oxygen. Are these science? No, they're mathematical truths that science presupposes. In his book, Stealing from God: Why Atheists Need God to Make their Case, Frank Turek does a fantastic job of going over this problem.
3. "All truth is relative/all morality is subjective": If all truth were relative, then why is the claimant making this claim if I can hear or see it? If all truth is relative, then so would the claim that all truth is relative be relative! Is it? Not if proclaimed publicly. The person telling me that I can't force my truth or my morals on him or her has just claimed objectively that all truth is relative, regardless of whether it's stated implicitly or explicitly — see the problem? The instant it's shouted out loud, this claim undergoes logical decoherence from truth to falsehood.
4. "All Christians are hypocrites": This claim commits the tu quoque fallacy, for starters. Just because its adherents are hypocrites doesn't mean it's not true. Secondly, who has the burden of coherence when it comes to living up to a moral standard? The one who makes up the standard in the first place, that's who. If there is no God, then morality is either relative or arbitrary. If it's relative, then point 3 applies. If it's arbitrarily defined by people, then those people have the burden of living up to the moral standards that they arbitrarily define. If they don't, then they're also hypocrites! They, therefore, cannot raise this charge if they're guilty of it themselves. Third, only some Christians are hypocrites, not all of them, which makes this a hasty generalization to boot.
5. "You shouldn't judge": Is this claim a judgment? You bet it is. It's a self-defeating judgment not to judge! But wait, didn't Jesus make this same judgment not to judge? Those who say this have committed the fallacy of quote mining. The passage in question is Matthew 7:1-5. In this same passage where Jesus says "judge not, lest you be judged," Jesus also tells us to "take the plank out of our own eye before taking the speck out of a brother's eye". Taking the speck out of another's eye is making a judgment, is it not? Jesus was simply telling us that if we judge, we must make sure we're not also guilty of the same thing that we're making the judgment about. Much different from the self-defeating claim of "don't judge, period".
There are, of course, countless others, but these are the most common ones. I hope that by posting this I can make sure fellow case-makers can be empowered to use this law of non-contradiction to debunk these rather silly (if thought about) claims — let's be clear: if one claims to be a beacon of reason only to make claims like these, he or she is doing a terrible job of living up to that reason claim.