Best launcher: ADW.Ex Launcher. Paid for, but worth the money, I've used it for over a year now, very customisable, very fast. Not sure if it'll make the cut when we eventually get ICS. It does have ICS presets, so I could make my phone look like ICS right now, but I don't want it to pretend to be something it's not. You can even replace the icons with this, so now I have a experience that looks 100% stock on my homescreen.
Best browser: Browser Guru. Not a 'browser' per say, but automatically launches Opera Mini when I'm on a slow 2G connection, and Dolphin HD when I'm on 3G or Wifi. Just one button on the homescreen, no messing about. Also opens links from e-mail etc with the correct browser. Such a beautifully simple but effective app. Love it.
Best gallery: Just using stock.
Music player: Never listen to music on my phone.
Video player: Stock. Tempted to try mxplayer.
3G Watchdog Pro - Stops me going over my usage limit for mobile data. Tells me which apps use the most data etc.
Juice Defender - Using the free version, I am able to save a fair bit of battery life with the "aggressive" profile, whilst still getting notifications and the like. Nothing in the paid version appealed to me, plus I can use AutomateIT to get most of the functionality that JuiceDefender Plus/Ultimate provides.
NFC Task Launcher - buggy at times and difficult to navigate, but once set up, it's pretty cool; tap the phone against a tag and perform an action. When I'm at work, and my phone is in my locker, I tap a tag in the locker to put it into airplane mode, which saves a ton of power, as it struggles to get a signal in there, which eats the battery somewhat. When I finally get my car holder set up, it will automatically put the phone into car dock mode, and will turn on bluetooth and turn off wifi...
AutomateIT Pro is a cracking app for making your phone Automate a lot of tasks. Currently it turns off WiFi when I'm not at home, puts on maximum brightness when my phone is plugged in, and silences notifications overnight.
Pulse is a brilliant news reader
BBC news is another good source of news
TED for good lectures
eBay, Amazon for shopping
Pocket - fantastic for saving things to 'read later' when on Wifi, home computer, or when I have more time.
Sygic - GPS Navigation
Glympse - Stops the missus phoning to ask where I am when I'm driving home.
Torque - For checking the state of my car's engine.
Easy Uninstaller - Gives you a list of installed apps that you can uninstall. This allows you to do batch uninstalls, which is a nice way of pruneing what you have installed quickly.
ConnectBot and AndroidVNC -- connecting to servers