Let me say it up front: this is my essential apps for Nexus 7, which may not apply to the others. Obvious I have my preference and I ignore things that I don't care. But if you find this list useful, let me know, and I will share more of my experience.
I got my Nexus 7 for a few days, and I was surprised by how much I enjoy using it. I give most of the credit to the 7 inch screen form factor, because this is what makes it different form my 4 inch screen Galaxy Nexus and my 10 inch screen New iPad. After trying out a lot of apps, here are the ones I found essential, the list of apps that I will definitely install/re-install when I facing with a clean machine or a factory-reseted machine.
Sync File with Cloud Service: FolderSync (Lite)
This application allows you to sync files and folders on your android device to big-name cloud services like Dropbox and Box.net. I use it to sync up emulator save games so that I can play a game on my Galaxy Nexus, and then continue that game on my Nexus 7.
PDF Reader: QuickOffice
Surprise! It's NOT Adobe Reader! I found the PDF rendering speed on QuickOffice really fast, good navigation as it provides thumb nail at the bottom. Adobe Reader is ok but just not as fast. I also tried a few other PDF reader and still find QuickOffice the best way to read PDF. My only complain is that I have to scroll the pages vertically. I perfer scrolling PDF horizontally so that it feels more like reading a real magazine. OfficeSuitePro and Aldiko support horizontal scrolling, but it wasn't smooth. Eventually I gave up and start trainning myself to scroll vertically.
File Explorer: ES File Explore
Fast, feature rich, allows me to move files around within the Andorid OR copy files to and from files on local LAN or even Cloud Drives like Dropbox and SkyDrive. MUST HAVE APPLICATION.
Music Player - Amazon MP3 Player
You see I am totally biased on this since I have a lot of music stored on Amazon Cloud Drive. And the player works great when playing mp3 files within the device (which I don't have a lot). However, I also like pausing a music or an audiobook or a podcast, and then come back later to continue. I found out that the best way to do it is having MULTIPLE players installs, and then install widget for each one of them, leave them on one home screen. That way each music player holds different kinds of content, and I can choose to continue one of them based on my mood. For instance, I use Amazon Mp3 PLayer to play music on the cloud, use MortPlayer Audiobook to play audiobook, use Winmap to play downloaded podcast, use Google Music to play music on the device .... I know, you might found this system a bit "too much". BUt it works for me.
eBook (ePub) reader : Aldiko
Works for English and Chinese ePub ebooks, support auto bookmarking. Such a must have to me. Make sure that when you open a ePub file in file Explorer (like ES File Explore), choose import o Aldiko instead of just open in Aldiko, because only imported ebooks support auto bookmarking.
Comics/Mange reader: Perfect Viewer
Support .cbr, .cbz, zip, rar and other manga and comics archieve format. Again, must have.
Photo browser: build in Photo Viewer or JustPictures!
I found the Google stock Photo Viewer great enough in most situation, but I also like have JustPicture! arrange stuff. So, try both and see which on you like better.
Game: Nesoid, SNEsoid, GBCoid, Gensoid, GameBoid
These are simulator for classic conolses like Nintendo Entertainment System, Super Nintendo, GameBoy Color, Genesis and GameBoy Advance. I am a sucker of emulator, and playing all these consoles on a 7 inch awesome screen is just like dream come true. My only complain is that I couldn't find a good gamepad add on to make my emulation experience complete. If you know of a good gamepad add on to either Nexus 7 or Galaxy Nexus, let me know.
Traditional Chinese Input: SCUT gPen Traditional Chinese input
My default Traditional Chinese handwriting input for both Nexus 7 and Galaxy Nexus. It does the job, and I don't have much complain.
Podcast Player: DoggCatcher
Yes, a paid app, but a good and worthy one. Otherwise, use Google Listen, but it's just more painful to maintain podcast feed in your Google Reader account.
PhotoFrame Widget on home screens: Turtle Photoframe
No nonsense setting, auto change photo file after a predefined period. This is a nice way to beautify your home screen using whatever photos you like (photos of your spouse, kids, dogs or whatever).
There are other choices, like Firefox, Opera, Dolphin HD ..... but I still like Chrome the most.
Note taking: Evernote
Dude, embrace cloud services.
Drawing: Sketchbook Pro
I brought it on iOS, and then got it for free at Amazon store. LOVE the app. If you love sketching, you need this app.
Cloud Service: Google Drive, Dropbox, Box.Net, SugarSync
INSTALL ALL for cry out cloud. Take advantage of all the cloud storage.
Social: Facebook, Twitter, Google+, Path
AGain, INSTALL ALL. Embrace social.
Instant Messenger: IMO
This is my universal Instant Messenger, supports Yahoo IM, Google Talk, MSN IM ...... As plan BCDE and F though, also install the individuality official clients just in case.
Wireless File Transfer: AirDroid
Awesome UI, easy to use, allows you to transfer files between your desktop computer and your Android device remotely using web browser on your desktop. Must have.
News Reader: Pulse, Flipboard, Zite
Use them as RSS Reader, or regular news reader. They are the reason why you brought Nexus 7: to read, and read a lot.
Office file manipulation: OfficeSuite or QuickOffice
I have both (brought one, and got another one for free). They both support cloud drives. If you want to manipulate your Word, Excel or PowerPoint document stored on the cloud drive, you need these applications.
Online Radio: Pandora, Tunein Radio, iHeartRadio
Well, they are all free, so why not install all of them.
Battery Indicator: Battery Status
I love to know exactly how much battery I have left on my device. Battery Staus does that by showing battery level in percentage on status bar, which is EXACTLY what I want.
Media Player: BSPlayer
This shit playing ALL freaking FILE FORMAT: mkv, rmvb, mpg, avi .... format that the build in player cannot play. Must have.
So that's it for now. Hope you love your Nexus 7 as much as I do.