For my Fluke 87-3 I have here at work:
I measured 890 ua in "on" mode, which strangely drifted to 972 as the meter was left on. (No back-light)
In standby mode, I measured 541uA, which drifted to 579ua in a few minutes. (strange, as I type this, it keeps going up. Ill edit my post if it ever stops - it keeps drifting)
I have no reason to suspect my Fluke 25 (with microampere range) is drifting, but I'll check again at home with some other meters.
EDIT:
I'm not sure what the peak was, as I was unable to watch it 100 percent of the time. I believe it got to 650 ua or so, then began to lower. It oscillated from 520 to 600 microamperes, and has finally settled at about 524 ua.