Opera Mobile(FREE) - Considered one of the best browsers on Android. Javascript processing is way faster than the stock browser.
Dolphin Browser HD(FREE) - Another very fast browser with a nice UI. Has some very nice plugins that can be added. This and Opera Mobile are probably the top 2 browsers on all of Android.
Chat Client Apps:
Trillian is probably your best bet for these unless you use the native GTalk only... Most of the others have some pretty hefty battery drain.
AOL Instant Messenger(FREE) GoSMS Pro(FREE) - A much better sms client than the native Messaging. Has popups and themes. (NOTE, you need to disable notifications in the native app if you don't want to get double notifications).
Meebo(FREE) Nimbuzz(FREE) Trillian(PAID) - Probably my favorite. Supports push to email as well.
Yahoo Messenger(FREE)
Launchers:
Launchers are replacements for your entire homescreen layout essentially.
Launcher Pro(FREE+PAID) - A very good home screen replacement launcher, however it seems it is no longer being updated. Paid unlock key required to use it's own widgets like FB + Twitter that are better than the native app widgets.
GoLauncher EX(FREE) - Probably my favorite launcher. Highly customizable, offers many downloadable widgets, themes, other apps made by the same company. You can also make your own Go Launcher themes.
Amazon MP3(FREE) - Amazon MP3 store/cloud service.
JetVD(FREE) - Allows you to search sites like youtube and download videos in HD to save locally.
MPlayer(FREE) - Supports a lot of various file formats.
Pandora(FREE) - Streaming customized radio stations.
PowerAmp(PAID) - Highly featured media player. Some like it more than Winamp, although it is a paid app.
Winamp(FREE) - Much better music player than the standard one. Has a widget that allows play/pause/ff/rw from the homescreen and has a widget that lets you change songs without unlocking the screen.
Movies:
Movies(PAID) - Very good app for movie theater info, showtimes, trailers, etc. Similar to the BB app.
News Apps (Non RSS):
Password/Secure Info Apps:
Passdroid(FREE) - An excellent random password generator + storage application. Most importantly this app does not require internet access permissions! A lot of password generators do...
Keepass(FREE) - Securely store and encrypt passwords or information. Has a desktop client and supports multiple mobile platforms.
Remote Desktop Apps:
Airdroid(FREE) - Allows you to access your phone through any web browser on the same wifi network with no additional software needed. Very nice.
LogMeIn Ignition(PAID) - Remote desktop application. Fairly expensive, but it has a lot of features and support.
Splashtop Remote Desktop(PAID) - Much cheaper than LogMeIn (1/5 the price), but it doesn't have as many features. No direct file transfer between your phone and the PC. It works fairly well though.
RSS Readers:
Feedr(PAID) - Very good RSS reader. Supports GR sync, searching for RSS feeds, ability to have particular feeds bypass GR sync, and widgets.
Google Reader(FREE) - Google's RSS reader. Works pretty well.
gReader Pro(PAID) - 3rd party actually made this app.
Newsrob(FREE) - Another highly regarded RSS reader.
Newsrob Pro(PAID) - Another highly regarded RSS reader. Pro version has no ads and additional features.
Pulse News Reader(PAID) - Very nice looking rss reader with a different, visual approach. The RSS and sync features are not as good as other apps though, but the visual appeal is quite nice.
Shopping:
Amazon(FREE) - Official Amazon app.
Ebay(FREE) - Official Ebay app.
Paypal(FREE) - Official Paypal app. Newest version supports NFC payments for NFC devices.
Social Networking Apps:
Facebook(FREE) - Official FB app for Android, works well enough. The LauncherPro FB widget is better than the FB app widget though.
Plume(FREE+PAID) - Has better widget options with multiple sizes. The only downside is that the refreshes seem to take a little longer than the native Twitter app.
TweetCaster(FREE+PAID) - Very nice twitter app, probably my favorite. Has a widget, supports themes and has a free and paid versions (free version is ad supported).
Travel Apps:
Poynt(FREE) - Local search for restaurants, events, bars, businesses, etc. Reviews, directions, weather, gas prices, etc.
TripIt (ads)(FREE) - Automatically aggregates your travel itinerary and syncs with your calendar.
TripIt(PAID) - Automatically aggregates your travel itinerary and syncs with your calendar.
Yelp(FREE)
Utility Apps:
Titanium Backup(FREE+PAID) - Must have tool imo. Allows easy backup + restore of apps and data, especially useful if you wipe and reload ROMs a lot. Paid version has more features like multiple backup copies per app, 1-click restore, dropbox support, etc.
Titanium Backup Pro Key(PAID) - Unlocks the pro features of TitaniumBackup. In order to use the paid version you have to install the free app, then buy and install the pro unlock key.
Apps Organizer(FREE) - Very useful tool. Allows you to categorize apps into labels that can be added as widgets (similar to a folder) on your desktop.
AnTuTu Benchmark(FREE) - Phone performance benchmark app that works on multi-core phones, unlike Quadrant.
Beautiful Widget(PAID) - A number of nice looking widgets for stuff like clocks, weather, skins, toggling radios, etc. Offers similar functionality to some of the HTC sense skin widgets.
Cloud Print(FREE) - Print directly from your phone using Googles cloud print service.
ColorNote(FREE) - A nice memo/notetaking application.
Dropbox(FREE) - Store and retrieve files to your online dropbox account.
Key Ring(FREE) - Store and use your various merchant loyalty cards from your phone.
Mileage(FREE) - Mileage tracker.
Mint(FREE) - Securely track expenses, bills, various accounts, etc.
Root Explorer(FREE) - Root access file browser to browse the entire android file system.
Speedtest(FREE) - Network speed test.
Volume+(PAID) - Great utility for applying Equalizer settings to your audio. Also supports increasing audio output volume for speaker, headset mode, and in-call volume (requires root).
Other Apps:
Live Wallpapers:
Doom Live Wallpaper(FREE) - Great live wallpaper from the game Doom that also supports some user interaction.
Haunted House HD(PAID) - Interactive haunted house with great graphics.
Drag Racing - Highly addictive drag racing game with online scores and multiplayer.
Grave Defense Holidays - Groundhog themed version of a zombie defense game. Pretty fun. There's also a gold version (PAID) that has 3x the levels and more towers.
Fruit Slice - Better version of Fruit Ninja imo and it's free. Graphics are much sharper than Fruit Ninja.
Pig Rush - Probably my favorite game, extremely simple concept and fun to pick up and play.
Sprinkle - Fun puzzle game.
Plants vs Zombies - Very fun, well made tower defense game.
Wordsmith Pro - A game similar to Words With Friends, but this game has no advertisements and you can only submit a word 3 times before forfeiting your turn (prevents people from trying words forever).