This is a list of some awesome Android apps and what they do. some will be paid and some will be free, if you have some apps you would like to add just respond and if the app is awesome I will add it to this post. Give this post a thumbs up if it helped you or if you discovered a new app and check back often, I'll keep adding new apps and updating this list.
Root apps and utilities
Rom Manager This is a must have app for anyone who is rooted, it is used to flash a custom recovery, make nand backups (makes a complete backup of your phone), lets you download and flash roms. The premium version removes ads and adds a couple more features.
Superuser You should already have this installed if you are rooted. I do suggest you get Superuser Elite just to donate to the people who maintain and update superuser. Plus it has OVER 9000!!! (It's a feature, deal with it).
BusyBox This is another app you should have installed if you are rooted. If you feel like it get the donate version and help support this developer.
Terminal Emulator You should already have this app if you are rooted. If you don't, install it now!
Tiatanium Backup This will back up all your apps, settings, text messages, phone history and anything else you can think of to your SD card. It is a lifesaver when updating or flashing a new rom when wiping the phone is necessary. You can also use this app to freeze or uninstall bloatware, move apps to external memory, make apps system apps, and sync your backups to dropbox for safekeeping. The paid version unlocks all of its features.
AppExtractor This is an awesome new app that lets you extract part of your rom manager nandroid backups. This is very useful if you would like to restore your text message history, apps, data or any combination of the three from your rom manager backups. The free version lets you restore up to five apps at a time while the paid version has no limits and will get new features as they come out.
Font Installer Lets you change your system fonts. Works well and has tons of fonts available.
SetCPU This cool app lets you over and under clock your CPU. Has tons of features like CPU scaling for performance, battery save and others. You can also create profiles for different scenarios like screen off and on and when the battery charge falls under a specified percentage and lots more. Recently the dev added voltage control for certain devices. With SetCPU you can unleash the maximum speed of your processor or just save some battery.
AdFree Android Want to get rid of ads in apps and when you are surfing the internet on your device? Just install this free app and they will disappear. This will help your apps and browser run a little faster because they wont be loading ads.
Wireless Tether If you are rooted this is the best app for tethering, its reliable and works with most phones and roms. If your carrier has blocked this app in the market you can find it here
SMS bomber Use this app if you want to send tons of text messages to someone. You can also remove the limit of 100 messages an hour with this app.
Bloat Freezer This useful utility lets you freeze the bloatware included with your phone without totally removing it. This app is great if you only have temporary root or want to be able to receive carrier updates. .
Autostarts This paid utility lets you stop apps from automatically starting up on their own. This works much better then any task killer.
Screenshot Apps (root required)
Screenshot This utility lets you take a screen shot and save it to your SD card. It's free and easy to use.
Screenshot it This is an excellent screenshot app, you can find the free trial version here the free trial is good for five screenshots. If you aren't rooted you can find the non root version here. *The non root version does require some setup. (App brought to my attention by King003
Non Root Utilities
This is the easiest (no root) tethering app to set up and use. It is backed by a great dev and worth the $4.99.
Privacy Blocker What this app does is amazing, it takes apps apart and looks at the code to see how the app is spying on you. It then spoofs that information in the apps code and puts the app back together for you to re-install. The free version Privacy Inspector lets you see what your apps are doing and accessing but won't take the apps apart and fix the problems.
Spare Parts Allows you to enable and change some hidden settings. The paid version gets new features before the free version.
Barcode Scanner Barcode scanners are useful for checking prices at stores, but you can also scan new barcodes to launch a web page or an app or add someones info to your contacts. This app is also used by some other apps.
WidgetLocker This is a fully customizable lockscreen replacement. You can add widgets and shortcuts to your lockscreen as well as customize sliders.
Root Explorer Awesome file manager it is fast stable and has tons of features I have never had one problem or crash using it. If you aren't rooted they have a free version called explorer it has all of the non rooted functions of root explorer and it's even ad free.
ES File Explorer This free file explorer has tons of features. Copying and moving files is just the beginning, this app also gives you the ability to sync to dropbox, backup your apps, transfer files via bluetooth, FTP client, text viewer and editor, document and image viewer, un RAR, ZIP and un ZIP and create encrypted (AES 256 bit) ZIP files. and more.
Thats right, your favorite file explorer is available for android. Its the first duel panel file explorer for android. Total commander is currently in beta so it's not in the market. Features include zip, unzip, unrar, search, FTP, bluetooth transfer, LAN access, single or duel panel mode, configurible tool bar, and all the basics (copy, move, delete, rename, etc).
Go SMS Pro Want more features and options from your messaging app? This is the answer, it has themes, Facebook chat, the ability to backup your SMS, an encrypted pin protected in box for those private conversations, and lots more. Its free has no ads and has been featured on XDA.
SMS Backup & Restore Want to keep a backup of your SMS conversations? This simple app will do just that, you can even send the backups to your email. (thanks for pointing this app out wolfster)
DeskSMS This is a new app from the devs that brought us cloclworkmod recovery and rom manager. This app lets you send and receive texts from a computer or tablet through plugins for Firefox and Google Chrome, or through Gmail or Google talk/chat. The app is free but using the service costs $4.99 a year to cover server costs and such, you do get a free trial so check it out.
One of the more popular launchers ADW is completely open source. It's packed with tons features. There is a reason Cyanogen
uses this as the launcher for his roms. Also available is ADWLauncher EX
which adds even more features to an already awesome launcher.
This is an awesome launcher for your Ice Cream Sandwich device. It has the great looks of the new homescreen style found in ICS with added functionality and more options. Some of the cool stuff includes scrolling dock, various screen transition effects, resize any widget, customizable app drawer, and gesture controls. It has tons more features, too many to list here. It is also very good looking and easy to use. It is free go try it out. If you like it the Pro Version
adds even more features.
This is the launcher created by the CyangogenMod team for Cyanogen 9. It is a clean looking ICS launcher with some additional options. It isn't complete at this time but it is still extremely smooth and very cool. It isn't available in the Play store yet due to the fact it is in beta, but you can download it from me.
This is the ultimate toolkit for network managment. Features include network discovery, service scan (TCP port scan), ping, traceroute, DNS lookup, Wake on LAN, TCP connection tester, MAC address and vendor gathering, customizable host names and icons, connectivity detection, geolocation, and integrated launch of third-party Apps for SSH, Telnet, FTP, FTPS, SFTP, SCP, HTTP, HTTPS, SAMBA.
Speed Test The most popular speed test app for a reason, its simple works well and looks good.
Network Diagnostic Tool This is an advanced speed and diagnostic test, it not only finds your upload and download speeds it will determine what problems are limiting your network speeds. This tool is generally for advanced users.
Carrier Coverage This app is a community project to make a map of the various carriers and their coverage, this map will be better and more accurate then any coverage map provided by the carriers since the map is made by actual users. This app is still in beta, if you want to contribute to this project install the app (link in title) and check out the forums.
If you are on ICS you should check out the beta for the mobile version of the Chrome browser. I have had some issues with it, but your mileage may vary.
Dolphin Browser This is one of the more popular browsers for Android, it has tons of features add ons, it is also smooth and easy to use.
Xmarks If you use this great service to keep your bookmarks synced now you can sync them to your phone. There is even an add-on for Dolphin Browser
Spotify Music lovers rejoice! Spotify has come to the United States, now you can have an all you can listen to music buffet for only $10 a month. Spotify has a huge selection of music and you can stream it to your device unlimited. They do have a free plan but you have to sync the music to your device manually from the computer rather then streaming it directly to your device.
tTorrent If you need to download a torrent but can't get to a computer this is the app for you. The free version is speed limited and ad supported, if you donate it removes both.
MoboPlayer This is a great video player, it can play lots of different video formats. It is the best video player I have found and its totally free.
Pulse This is an awesome app for reading the news. It's easy to use and looks great.
Nook The nook app from Barnes & Noble is a solid book reader for your Android device. Barnes & Noble has a huge selection of books and the app also lets you sideload your own books in the ePub format. You can even borrow books from the library and share a book with a friend.
Swype Love it or hate it Swype is a fast way to type. If your phone didn't come with Swype pre installed or you lost it when you flashed a custom rom, clicking on the link will take you to the sign up page for the Swype standalone app,
SwiftKey X This awesome keyboard takes predictive texting to the next level by guessing the next word you are going to type before you even type it. This keyboard will learn how you type to make predictions more accurate.
Emulators We all love emulators, unfortunately great ones are hard to find especially since a bunch have been removed from the market. Here are a few great emulators that work great and they are free (for now). Get em free while you can!
If you can imagine it you can build it! Now minecraft is on your phone, get it before Notch raises the price! Free demo version here
World of Goo
In this game you use the little living black balls of goo to make structures, bridges, and objects to get them through the level. It is great fun and there is even a free demo version available.
Visidon AppLock Want facial recognition to keep your apps safe? Well this is the app for you. Its an awsome app, great for impressing your friends or just feeling like a secret agent.
Prey Anti Theft No one expects to have their device stolen, but if it does happen you will want Prey installed. With it you can track the phone's location, remote wipe, send the thief a message and more. Best of all its totally free and open source.
Remote for iTunes When I switched from the iPhone to Android there was a couple things I did miss, using my phone as a remote for iTunes was one of them. This app adds that function and is a lot like the remote app from apple for the iPhone.
Samsung Remote If you own a Samsung Smart TV download this app and use your Android phone as a remote for it. The tablet version can be found here. Samsung even has a better remote for Samsung devices called Samsung Smart View, it adds the ability to share content between the phone and TV. If you want the Smart View app and don't have a Samsung phone just click here and downloaded the version modded to work on any Android phone.