Post your favourite apps, tell us why you like it and please include a link!
My current favourite by all is Spotfy, after I bit the bullet and forked out for Premium so I could use the Android app. Absolutely love having so much music to hand, to play offline, and its a much better music app than the standard app on the phone.
Tapatalk is also a favourite, making forum browsing a doddle.
Doggcaster is a great podcast app, worth the few dollars I paid for it.
And absolutely essential is Mybackup Pro, which takes automatic backups online or to SD card and just restores the entire system, messages etc effortlessly should you ever need to do a hard reset.
Gmote - works as a remote control for VLC player via wifi.
Handcent SMS - much slicker than standard HTC SMS app
SlideIT keyboard - took a bit of time to get used to, but now its much faster than tap typing
MagicMarker - neon etch-a-sketch. Keep kids entertained, or just use it for insulting mates across a pub without shouting
LED scroller 3 - as above, although not so good for keeping kids entertained
ConvertDroid- quick way to convert units
gvSIG mini maps. Like Google maps, but with OS mapping - handy for checking whether green lanes are legal
Appbrain - browse apps and choose which ones to install from a pc - then just sync and let the phone get on with it.
Barcode Scanner - only ever used for QR codes. Don't think I've needed it since I got Appbrain
myPlayer - limited BBC iPlayer access.
Photobucket mobile - was a pain when it automatically tried to upload every pic I took without asking, but really handy since I turned that off.
Catch notes - handy to have somewhere to scribble down stuff without having to send a SMS to myself
Astrid task/todo list
opera mini - rarely use unless in a bad signal area - server side compression makes it faster than std browser over a slow connection. Not good enough to use all the time though.
Google Sky Map - both of these two are of pretty much zero practical use to me, apart from freaking out old people and technophobes. For which reason I like 'em
Just downloaded "Keyboard from Android 2.3" by Steven Lin (free) - it's superb! (imo)
Cinedroid good for the cinema
British Airways App is great for checking in and having an E boarding pass on your phone
Zedge for ringtones
I've been bingeing on GO Dev apps lately.
Handcent got binned in favour of GO SMS Pro when I changed phone and wanted to back up all my texts to the SD card and then restore them onto the new phone. Seemed at least as good as Handcent at everything else, and had a decent backup/restore feature as well.
From there I tried GO Contacts. Not a massive revolution over the stock Android contact manager, but just a bit more slick and nice to use.
GO Keyboard was the next one I tried. Seemed like a nice improvement over the standard type keyboards, but having used Swype and SlideIT, I found it really hard to go back to the old tappy type keyboards. I've gone back to using Swype again now. Bit of a pain to install as you have to register for the beta program, then download an installer program which downloads the actual keyboard once you've authenticated your account. Royal pain in the arse, but it's well worth it - by far the best of any of the Android keyboards I've used.
The last one I've tried is GO Launcher Ex. Seems more stable than ADW launcher which I was using previously, and seems as slick and polished as the rest of the GO apps too. It's also got a task killer built in. I know you're not really meant to need a task killer with Android, but sometimes a poorly written app can cause things to slow down, and it's handy to be able to just kill all of them to get control back instantly rather than faffing about waiting for Android to do it's thing in the background.
Notification Toggle is a new favourite too - it lets you put switches for various functions in the notifications window. It's so much more convenient to be able to quickly change stuff like wifi or flashlight on/off without having to leave an app and go back to the home screen.
TuneIn Radio is brilliant for internet radio - and it lets you create an account to remember your favourite station "presets", so you have them available on your computer via tunein.com or on any of your android/iphone/ipod touch type doodads.
WiFi Analyzer has been really useful for me at work too - shows all nearby wifi signals and which channel they're on. Great for troubleshooting and avoiding frequency clashes etc.