My hair is naturally a medium ash brown, and I dye it a shade or two darker because it looks nicer on me and matches my naturally dark brows.
I started by using Nice n' Easy 121A - Natural Deep Brown. Just a warning for those going for a rich brown, this colour is actually a BLACK. Not a blue-black, but a black nonetheless. It also dyes your skin and doesn't come off for days. The great thing about it, however, is that it does. not. fade. Which is great if that's the colour you're looking for -- unfortunately, it wasn't for me.
That was about a year ago now, and I've spent my time trying to transition my hair back to a dark brown while the black grows out. I first tried to transition with 120 -- and got HOT orange roots. Beware. I figured, since it was only one "number" up from 121A, it would be close enough -- nope. Strike two, try again.
Finally, I've settled on 131 - Dark Brown. It is the colour I was originally looking for.