If you decide to purchase a single application for you Android phone, let it be Tasker. Tasker is an application for Android which performs Tasks based on Contexts (application, time, date, location, event, gesture) in user-defined Profiles, or in clickable or timer home screen widgets.
This simple concept profoundly extends your control of your Android device and it's capabilities, without the need for 'root' or a special home screen. Tasker can basically do anything you can images with your phone triggered by any trigger you can imagine. And it's continuously updated with new features.
A few of the endless range of things you can use Tasker for includes: Password protect applications, wake up with a random song from your music collection, change all of you home icons and wallpaper based on your location, make automatic recordings of what you say during phone calls to the SD card or launch an application automatically when you connect headphones to your phone.
￼Of the many tasks I've created my personal favorites are these two: If my phone is connected to a charger, it is muted between 10 pm and 8 am. This means that my phone will automatically be muted when I plug it in before going to bed at night, but sound will be turned back on before I get up in the morning. Further, if anybody in my family calls during the night, the phone will automatically turn sound on for five minutes and play a loud ringtone. So even though my phone is automatically muted at night, my family can still reach me in case of an emergency.
My second favorite task is a location task based on WLAN. If my phone is connected to the WLAN at home or at work when an SMS is received it will send a TCP request to my workstation (different one at home and at work). On my workstations I run a small script that receives the requests and shows a popup on the screen containing the content of the SMS and who sent it. If the SMS contains a one time password for any of the services I use, the popup is persistent, and contains a button that automatically copies the one time password to the copy ring on my workstation, so I can paste it directly.
The possibilities are endless. You can see a great tour of the features of Tasker here. Understanding how to use Tasker, and how to create new tasks takes a little bit of getting used to. But once you have learned the system, it's actually very easy. Be warned though. This is not an entry level application. Don't expect to download it, install it, click two buttons and be done with it.
I do recommend purchasing the application directly from the website (you get a free 7 day trial), rather than purchasing it from Android Market. If you purchase it directly, the developer gets a greater share of the money, and you get some additional encryption features that cannot be offered through Android Market.
So if you don't completely suck at logic, and you don't mind spending time learning the interface, Tasker will turn your phone into an extremely powerful device that makes iPhones, Symbians and all of the others look like baby toys. One final teaser: Thanks to Tasker and X10 I control the lights in my apartment simply by touching a couple of icons on my phones home screen.