My shiny new bike developed a soft 'cluttering' sound; like a clatter but quieter. Took it back to the shop I bought it from, and he discovered a couple of very loose spokes. All better!

DH's mysterious ticking sound was never diagnosed, but after replacing his bottom bracket, and taking apart and lubing his rear hub, possibly some hair-pulling, it has finally vanished. Reminds me of this, because I'm a nerd.