The one I hear the most, and perhaps the most annoying, is the perennial favorite "if man came from monkeys, why are there still monkeys?" I usually respond with "if Mexicans came from Spain, why are there still Spaniards?"
The more interesting are the ones thst delve into specific examples of "design" such as the eye or the bird wing or bat sonar or the bacterial flagellum, and declare that these could not possibly have evolved by natural processes. Since I've started hubbing, I find these to be a great writing opportunity - I'm working on a hub about bat echolocation that I hope to publish tomorrow for Darwin Day.
The information theory questions are pretty popular - how can mutations create information/beneficial structures/etc.
Then there are the ones based in taxonomy - how can evolution produce new "kinds," or why has evolution never produced a crocoduck (which it has).
Also infuriating are the AIG/CI arguments that use real science and false dichotomies to argue for a young Earth. For example, when scientists find fossilized protein residues in a dinosaur skeleton, the creationists argue that protein can't possibly last millions of years, therefore dinosaurs are only 6,000 years old.
Perhaps most annoying are the ones that are based heavily in anthropic principles. The Comfort/Cameron banana argument is one of these - evolution could not have produced the banana, which was obviously designed by an intelligent designer to fit human hands. (There's a grain of truth to this one, as the modern banana is a product of intelligent design by human farmers by hybridization and selective grafting. The wild banana is an unpalatable seed-pod)
That's just a small sample - haven't even delved into the second law of thermodynamics or abiogenesis yet. There's just too much antiscience to list them all.