I have Nexus 7(7") and Acer a500 (10").
I will write down apps I actually use daily. Not apps I have it installed but rarely use, such as Shazam.
Btw, I am a tech geek, don't like to play games, and like taking photos.
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Here's my list:
Social Frame HD - Photographers (or ppl who has lots of photos) will love this app! Turns your tablet into a digital photo frame. Not only you can view photos that are copied into the tablet, but also photos from Facebook Album will be synced to your device.
BeyondPod - Best podcast app ever! I watch cnet news and nbc nightly news everyday with this. Do you have any other podcast you suggests?
MX Player - Best video app. I watch movie with this. I hook up with HDMI cable to watch in bigger monitor/TV.
Pocket - Using a desktop PC, whenever I come across a good article but long

, I pocket using chrome extension. It syncs article into my tablet so that I can read later offline on my tablet. I use this app often when I am outside (no internet).
Adobe Reader - Read e-books. The reason I bought tablet.
App Lock - When you have a tablet and carry it around, friends (or friends' kids) sometimes asks to play around with it. You want to lock apps that are private (gmail, facebook, google play (so that others cannot mistakenly(?) purchase paid apps), settings, and etc.)
Pulse - I use many news reading apps. Pulse , Feedly , Flipboard, and Currents. I can't say which one is better. They have their own advantages and disadvantages. I select which one to use depending on my use. I use pulse when I am lazy but want to update news quickly by just reading 'Best of technology' and 'Best of News'.