391 was my best for my game, I published it 4 days ago!
About 1500, but it didn’t last more than a few days.
I once got 1200 or 1300 in… Amazon AppStore - because my game was the only one of its type that was compatible with Kindle Fire at the time when it was first released. Soon other developers discovered how to make their games also compatible (it was “largeScreens=true”) and now I get maybe 30 downloads a day there or less. 
I got 477 downloads on Google Play on 6 August!
It was because my game get reviewed by a popular Italian website.
716 yesterday ^^!
and 133 uninstallations d’oh!
73000 with wallpaper app 
50,000ish…
Wow… I’m really not in the same league with some of you, but here are my records anyway:
Color Match Free: 5
Shape Fitter Free: 14
Shape Fitter: 1
Rhythm Sheep Free: 19
And a new record for a paid app from last Saturday… 
Rhythm Sheep: 2
436 for a flashlight
62.000+ last week
34,720 Downloads
In 2011 we had ca. 80k / day for one of the games but it was featured by GPlay so not entirely organic.
Nearly 5k installs per day for one app.
slightly off-topic: I wonder if an app that has push or icon ads has chances to be featured in the market.
About 11000 on Christmas day 2012, over 6k just from the Amazon marketplace. If only I could get that every day!
33158 for Caller Name Talker on Jan 9th. My app had the 8th position in the Top Free apps list in India. Now averages around 3k/day
You’re all big league, guys. My record is 450 (or so) dl/day for a few days for a memory training game, but now it’s back down to between 150 and 250.
70k / day when featured on Google Play. That was over a year ago. I bet its even more now.
223,000 
a lot of apps though.
Paid app around 30 in a day
Free app around 2,000 in a day
30k . still i don’t know how it happened. it’s a simple app with push ads. i got tons of german traffic within couple of days.