They can be classic - for instance the famous H. Huntsman single-button suits, or a single breasted single button model with a peak lapel (as long as the cut is tasteful.) But you will need to exercise extreme caution as most single button suits out there are awful designer versions.
I have an excellent Valentino black one button. The cut is very classy, but is stylish enough that it looks great during night time events or even upscale clubs. The pants are flat front and uncuffed. The overall fit is slim. I prefer to wear it with an open collared shirt and chelsea boots.