Here are some applications that no self respecting Symbian user should be without...
Most of these apps are either free or low-cost, but some of them aren't so cheap... but worth it...
FExplorer - A file manager application for the phone, which is much better than the default file browser on the phone. You need to sign the application with your phone's IMEI number to allow it to access your phone, but it's a simple process.
FlipSilent - This program is amazingly useful if your phone has a motion sensor, you're going into a meeting or somewhere that you don't want to be disturbed by your phone, simply flip your phone over, and put it down, face-fown and the application puts your phone into silent mode. Can also be used to snooze or stop your alarm or silence / reject a call with the same gesture.
Handy Profiles - This program uses rules that you set up to change the profile (Ring tone, Sms tone, Volume & Vibration). So you can automatically change the profile of your phone based on the time of day or calendar entries. It also supports changing profiles based on which cell you are in, allowing different profiles for home and work.
Handy Taskman - This program replaces the built-in task manager with more features. Also shows the available resources: RAM, Phone memory usage and SD card memory usage.
SMS & MMS Diary - Symbian phones allow for unlimited sms & mms storage, as long as there's free space you can store messages, so your phone will fill up eventually. There is no native way to store these messages anywhere but in your phone, but this application can back them up to HTML / Plain Text files allowing you to store your messages.
Garmin Mobile XT - This application allows your GPS-enabled (or connected to bluetooth GPS receiver) cellphone to act almost exactly just like a true Garmin device...
There are lots more applications out there, some are very useful and some have excellent gimmick potential, from blocking calls from certain people to using the phone's IR transmitter to turn off any TV you point it at...
Most of them you can find with a simple google search or by checking out some of the forums....