Note: All apps are free (or atleast have a lite version/ad supported) and are available at the Android Market. More apps/categories will be added :)
Android Market alternatives:
Appbrain app market: Excellent alternative to the standard android market http://www.appbrain.com/app/appbrain...demonkeys.apps
and
Fast Web Installer: Required if you want to install apps from the computer's browser. http://www.appbrain.com/app/fast-web...keys.apppusher
Communication and Internet:
Call/Message Blocking:
Easy Filter (Removed from the market. Thanks Avinash for the tip)
Data based Calling: (free calls via Internet, read the ToS of app before using)
Skype https://market.android.com/details?id=com.skype.raider
Contacts:
Dialer 2: https://market.android.com/details?i...=search_result
Go Contacts https://market.android.com/details?i...jbapps.contact
Ray Dialer: https://market.android.com/details?i...=search_result
Touchpal dialer: https://market.android.com/details?i...=search_result
Data Usage Monitoring:
3G Watchdog https://market.android.com/details?i...oid.g3watchdog
Dialer:
Go Dialer (part of Go Contacts, look above for the link)
Dialer One https://market.android.com/details?id=kz.mek.DialerOne
Messaging: aka SMS/Texting
Handcent SMS https://market.android.com/details?i...ndcent.nextsms
GO SMS https://market.android.com/details?id=com.jb.gosms
Browser:
Dolphin HD https://market.android.com/developer...olphin+Browser
SkyFire https://market.android.com/developer?pub=Skyfire
Opera Mini https://market.android.com/developer...a+Software+ASA
Opera Mobile https://market.android.com/details?id=com.opera.browser
Social networking:
Twitter for Android https://market.android.com/developer?pub=Twitter,+Inc.
TweetDeck https://market.android.com/details?i...ck.android.app
Twidroyd https://market.android.com/details?id=com.twidroid
Seesmic https://market.android.com/developer?pub=Seesmic
Plume https://market.android.com/details?i...velup.touiteur
Tweetcaster https://market.android.com/developer?pub=Handmark
Tools:
Alternate Keyboard: (Can be installed alongside other Keyboards)
Swype (beta) https://beta.swype.com/
Better Android (options cannot be altered in the free version) https://market.android.com/developer?pub=Better+Android
Go Keyboard https://market.android.com/details?id=com.jb.gokeyboard
MessagEase https://market.android.com/details?id=com.exideas.mekb
AI Type Keyboard https://market.android.com/details?i...aitype.android
Smart Keyboard Trial (nag screen) https://market.android.com/details?i...=search_result
Thick Buttons https://market.android.com/details?id=com.thickbuttons
TouchPal Keyboard https://market.android.com/details?i...k.smartinputv5
Multiling Keyboard (supports many languages) https://market.android.com/details?i...klye.ime.latin
Anysoft Keyboard: (also supports multiple languages) https://market.android.com/details?i...nysoftkeyboard
Hacker's Keyboard: (has arrow keys, esc, ctrl) https://market.android.com/details?i...ion.pckeyboard
Gingerbread Keyboard (Keyboard from Android 2.3) https://market.android.com/details?i...e=related_apps
Antimalware:
Lookout Mobile Security https://market.android.com/details?id=com.lookout
Anti0-virus Free (AVG) https://market.android.com/details?id=com.antivirus
Application managers:
App2SD https://market.android.com/details?i....gphone.app2sd
Appkik https://market.android.com/details?id=com.diune.appkik
App cleaner:
1 Tap Cleaner https://market.android.com/details?i...phone.acc.free
Android Assistant https://market.android.com/details?i...processmanager
History Eraser https://market.android.com/details?i...nfolife.eraser
Easy Uninstaller https://market.android.com/details?i...fe.uninstaller
Battery monitoring/saving tools:
Battery Dr to Save Battery https://market.android.com/details?i....batterydoctor
Juice Defender https://market.android.com/developer?pub=Latedroid
File Managers:
ASTRO File Manager https://market.android.com/details?i...ature=top-free
File Expert https://market.android.com/details?id=xcxin.filexpert
Explorer https://market.android.com/developer?pub=Speed+Software
ES File Explorer https://market.android.com/details?i...gs.android.pop
Backup Apps:
Dropbox: Official Dropbox app for android https://market.android.com/details?i...=search_result
SMS Backup & Restore: Backs up your text messages as an xml file. https://market.android.com/details?i...=search_result
Sugarsync: Official app for Sugarsync app https://market.android.com/details?i...=search_result
Wuala: Official app for Wuala https://market.android.com/details?i...=search_result
Productivity:
(a) Dictionary:
Merriam-webster Dictionary: Best offline dictionary tool. And its the official Android app form Merriam-Webster https://market.android.com/details?i...=search_result
(b) PDF/Ebook readers:
Adobe Reader https://market.android.com/developer?pub=Adobe+Systems
FB Reader https://market.android.com/details?i...ary.ui.android
Calculators/Text Editors/Password managers:
Handy Calc: Calculator with scientific mode,converter,etc https://market.android.com/details?i...=search_result
Jota Text Editor: Excellent text Editor https://market.android.com/details?i...=search_result
KeePassDroid: Keepass for Android. https://market.android.com/details?i...=search_result
(tip: use a backup app like dropbox to sync password database between PC/Phone)
System tools:
Androidlost: Lost phone tracker https://market.android.com/details?i...=search_result
Bluetooth file transfer: File manager with bluetooth support to browse/transfer apps between devices https://market.android.com/details?i...=search_result
Battery Indicator: Indicates battery status such as voltage,temperature, health, time unplugged etc in the status bar. https://market.android.com/details?i...=search_result
My Data Manager Free: Mobile Data Usage monitor https://market.android.com/details?i...=search_result
Network Info II: Complete info about tour network/wi-fi/bluettoth, etc https://market.android.com/details?i...=search_result
Reminder/Alarm:
Colornote Notepad Notes: Note taking app https://market.android.com/details?i...=search_result
ZDClock: Alarm clock, Hourly Chime, Reminder, etc https://market.android.com/details?i...=search_result
Task Managers:
If you have Android 2.1 or > you don't need a Task manager, certain apps run like services and start up in a few seconds if you kill them. I am just listing them here in case you have older versions of Android
Advanced Task Killer https://market.android.com/details?i...ature=top-free
SystemPanelLite Task Manager https://market.android.com/details?i...pp.systempanel
Task Panel Xtra https://market.android.com/details?id=sychee.taskpanel
Process/App Monitor:
Use this instead of Task managers.
Watchdog Task Manager Lite https://market.android.com/details?i...t.watchdoglite
Multimedia:
Photography:
(a) Camera tools/pic editors
FX Camera https://market.android.com/details?i...droid.fxcamera
lgCamera https://market.android.com/details?i...epper.lgCamera
Little Photo: Camera app https://market.android.com/details?i...=search_result
PicSay: Photo Editor https://market.android.com/details?i...=search_result
QuickPic: Image browser/gallery https://market.android.com/details?i...=search_result
(b) Document Scanner:
Cam Scanner https://market.android.com/details?i...sig.camscanner
(c) Bar code/ QR code scanner:
Barcode Scanner https://market.android.com/details?i...client.android
QR Droid https://market.android.com/details?id=la.droid.qr
(d)Screenshot app:
Shootme (ROOT required, but works on certain un-rooted phones) https://market.android.com/details?i...bw.picme.local
NOTE: More apps are listed in Post #4 due to text character limits in vbulletin ----> http://www.avinashtech.net/android/2198.htm#post13232