there are many of the common fluorescent dyes used to detect and quantitate DNA. like DAPI, Hoechst Dyes, PicoGreen, RiboGreen, OliGreen, and cyanine dyes such as YO-YO, ethidium bromide, and SybrGreen. The colour of some of these dyes changes with concentration of nucleic acids.
let me make a minor correction to Vikas kumar Patel, the color of the dyes don't actually change, but their fluorescent properties do. You generally have to excite at a certain wavelength (often in the UV range) in order to observe a color emission in the visible wavelength. I am not aware of any molecules that change color upon binding without requiring excitation to observe. But the list of dyes he has are the normal ones used for DNA detection.
The gold nanoparticles change from blue to red and vice versa. A single strand of DNA is attached to the nanoparticle, and when the complementary strand binds, it changes color. People use these particles for sensing devices.