I have good relative pitch... not perfect by any stretch of the imagination, I can hear when I get pitchy (as they say on American Idol) and since I'm out of practice without any formal training anymore, I make a lot of the typical vocal errors.
To the average person, I sound dead on though... but to me, I can tell that I'm a little bit off on some transitions. I can control my vibrato decently for being so outta practice. I can't sing in tenths of a tone or other crazy crap like that... but I can hear it, but only sing toward the correct pitch. I knew some people in college that were able to sing in 1/16ths of a tone. :Q
I'm about as good as some of the last 64/32 contestants on American Idol... but that's not saying much. They were in key but made vocal errors too. Heck, if you listen to Christina Aguilera in the studio (MTV Diary) you notice she's correcting herself a lot even though a lot of people I know said it sounded fine.